Dugald Stewart - Elements of The Philosophy Of the Human Mind Volume 2

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SHELF N°

.ÂDAMS

ELEMENTS

OF THE

PHILOSOPHY OF THE HUMAN MIND.

ELEMENTSOF THE

PHILOSOPHYOF THE

HUMAN MINDBY

DUGALD STEWART, Esq. F.R. SS. Lond. & Edin.

HONORARY MEMBER OF THE IMPERIAL ACADEMY OF SCIENCES

AT ST PETERSBURGH ;

MEMBER OF THE ROYAL ACADEMY OF BERLIN ;

AND OF THE AMERICAN PHILOSOPHICAL SOCIETY HELDAT PHILADELPHIA

;

FORMERLY PROFESSOR OF MORAL PHILOSOPHY IN THEUNIVERSITY OF EDINBURGH.

VOLUME SECOND.

SECOND EDITION.

EDINBURGH

:

Printed by George Ramsay and Company,FOR ARCHIBALD CONSTABLE AND COMPANY, EDINBURGH;

AND CADELL AND DA VIES, LONDON.

1816. ./

ADVERTISEMENT.

After an interval of more than twenty

years, I venture to present to the public a

Second Volume on the Philosophy of the

Human Mind.

When the preceding Part was sent to the

press, I expected that a few short chapters

would comprehend all that I had further to

offer concerning the Intellectual Powers

;

and that I should be able to employ the

greater part of this Volume in examining

those principles of our constitution, which

are immediately connected with the Theory

of Morals. On proceeding, however, to at-

tempt an analysis of Reason, in the more

strict acceptation of that term, I found so

many doubts crowding on me with respect

to the logical doctrines then generally receiv-

ed, that 1 was forced to abandon the com-

paratively limited plan according to which

I had originally intended to treat of the Un-

VI ADVERTISEMENT.

derstanding, and, in the mean time, to sus-

pend the conlinualion of my work, till a

more unbroken leisure should allow me to

resume it with a less divided attention.

Of the accidents which have since occur-

red to retard my pros^ress, it is unnecessary

to take any notice here. I allude to them,

merely as an apology for those defects of

method, which are the natural, and perhaps

the unavoidable, consequences of the fre-

quent interruptions by which the train of

my thoughts has been diverted to other pur-

suits. Such of my readers as are able to

judge how \ery large a proportion of mymaterials has been the fruit of my own me-

ditations ; and who are aware of the fugi-

tive nature of our reasonings concerning phe-

nomena so far removed from the perceptions

of Sense, will easily conceive the difficulty I

must occasionally have experienced, in de-

cyphering the short and slight hints on these

topics, which 1 had committed to writing at

remote periods of my life ; and still more, in

recovering the thread which had at first con-

nected them together in the order of my re-

searches.

I have repeatedly had occasion to regret

the tendency of this intermitted and irregu-

ADVERTISEMENT. vU

Jar mode of composition, to deprive my spe-

culations of those advantages, in point of

continuity, which, to the utmost of my power,

1 have endeavoured to give them. But I

would willingly indulge the hope, that this

is a blemish more hkely to meet the eye of

the author than of the reader ; and I amconfident, that the critic who shall honour

me with a sufficient degree of attention, to

detect it where it may occur, will not be in-

clined to treat it with an undue severity.

A Third Volume (of which the chief ma-terials areaheady prepared) will comprehendall that I mean to publish under the title of

the Philosophy of the Human Mind. Theprincipal subjects allotted for it are Lan-

guage ; Imitation ; the Varieties of Intellec-

tual Character; and the Faculties by which

Man is distinguished from the lower animals.

The two first of these articles belong, in strict

propriety, to this second part of my work

;

but the size of the volume has prevented mefrom entering on the consideration of them

at present.

The circumstances which have so Ions de-

layed the publication of these volumes on

the Intellectual Powers have not operated,

in an equal degree, to prevent the prosecu-

Viii ADVERTISEMENT.

tion of my inquiries into those principles of

Human Nature, to which my attention was,

for many years, statedly and forcibly called

by my official duty. Much, indeed, still re-

mains to be done in maturing, digesting, and

arranging many of the doctrines which I was

accustomed to introduce into my lectures;

but if I shall be blessed, for a few years

longer, with a moderate share of health and

of mental vigour, I do not altogether despair

of yet contributing something, in theform of

Ebsai/s, to fill up the outline which the san-

gmne imagination of youth encouraged meto conceive, before 1 had duly measured the

magnitude of my undt^rtaking with the time

or with the abilities which I could devote to

the execution.

The volume which I now publish is more

particularly intended for the use of Acade-

mical Students ; and is offered to them as a

guide or assistant, at that important stage

of their progress when, the usual course of

discipline being coiii pitted, an inquisitive

mind is naturally led to review its past at-

tainments, and to form plans for its future

improvement. In the prosecution of this de-

sign, 1 have not aimed at the establishment

of new theories ; lar less have I aspired to

ADVERTISEMENT. ix

the invention of any new organ for the dis-

covery of truth. My principal object is to

aid my readers in unlearning the scholastic

errors which, in a greater or less degree, still

maintain their ground in our most celebrat-

ed seals of learning ; and by subjecting to

free, but, I trust, not sceptical discussion, the

more enlightened though discordant systems

of modern Logicians, to accustom the un-

derstanding to the unlettered exercise of its

native capacities. That several of the views

opened in the following pages appear to my-self origmal, and of some importance, I will

not deny ; but the reception these may meet

with, I shall regard as a matter of compara-

tive indifference, ifmy labours be found use-

ful in training ihe mind to those habits of re-

flection on its own operations, which mayenable it to superadd to the instructions of

the schools, that higher education which no

schools can bestow.

Kinncil-House, 29.d November 1813.

CONTENTS.

of reason, or the understanding properly so

called; and the various faculties and opera-

tions MORE immediately CONNECTED WITH IT, Page I

Preliminary Observations on the Vagueness and Ambiguity

of the common Philosophical Language relative to this

part of our Constitution.—Reason and Reasoning,—

Understanding,—Intellect,—Judgment, &c. - ib,

CHAP. I.

Of i/ie Fundamental Latvs of Human Belief; or the Pri-

mary Elements of Human Reason, - 27

Sect. I.—Of Mathematical Axioms, - - 28

I. .... ib.

II. Continuation of the same Subject, - 46

II.—Of certain Laws of Belief, inseparably connect-

ed with the exercise of Consciousness, Me-

mory, Perception, and Reasoning, - 52

III,—Continuation of the Subject.—Critical Remarks

on some late Controversies to which it has

given rise.—Of the Appeals which Dr Reid

and some other Modern Writers have made,

in their Philosophical Discussions, to Com-

mon Sense, as a Criterion of Truth, - 68

1

Xll CONTENTS.

CHAP. II.

Of Reasoning and ofDeductive Evidence.

Sect. I. - - - - . Page 9*

I. Doubts with respect to Locke's Distinc-

tion between the Powers of Intuition and

of Reasoning, - - - ib.

II. Conclusions obtained by a Process of De-

uction often mistaken for Intuitive Judg-

ments, - - - - 103

II.—Of General Reasoning, - - 109

I. Illustrations of some Remarks formerly

stated in treating of Abstraction, - ib.

II. Continuation of the Subject.—Of Lan-

guage considered as an Instrument of

Thought, - - - 133

III. Continuation of the Subject,—Visionary

Theories of some Logicians, occasioned

by their inattention to the Essential Dis-

tinction between Mathematics and other

Sciences, . - .> 142

IV. Continuation of the Subject.—Peculiar and

siipereminent Advantages possessed by Ma-

thematicians, in consequence of their de-

finite Phraseology, - - 152

III.—Of Mathematical Demonstration, - 155

I. Of the Circumstance on which Demonstra-

tive Evidence essentially depends, - ib.

11. Continuation of the Subject.—How far it

is true that all Mathematical Evidence is

resolvable into Identical Propositions, 170

III, Continuation of theSubject.—Evidence of

the Mechanical Philosophy, not to be con-

founded with that wliich is properly call-

ed Demonstrative or iSIathiynatical.—Op-

posite Error of some late Writers, - 185

I v.—Of our Reasonings concerning Probable or Con-

tingent Truths, - - - - 213

CONTENTS. Xni

I. Narrow Field of Demonstrative Evidence.

—Of Demonstrative Evidence, when com-

bined with that of Sense, as in Practical

Geometry ; and with those of Sense and of

Induction, as in the Mechanical Philoso-

phy.—Remarks on a Fundamental Law of

Belief, involved in all our Reasonings con-

cerning Contingent Truths, - Page 213

II. Continuation of the Subject—Of that

Permanence or Stability in the Order of

Nature, which is presupposed in our Rea-

sonings concerning Contingent Truths, 220

III. Continuation of the Subject.—General Re-

marks on the Difference between the Evi-

dence of Experience and that of Analogy, 239

IV. Continuation of the Subject.—Evidence of

Testimony tacitly recognised as a ground

of Belief, in our most certain Conclusions

concerning Contingent Truths.—Differ-

ence between the logical and the popular

meanings of the word Probability, - 251

CHAP. III.

Ojthe Aristotelian Logic.

Sect. I.—-Of the Demonstrations of the Syllogistic Rules

given by Aristotle and his Commentators, 257

II.—General Reflections on the Aim of the Aristo-

telian Logic, and on the Intellectual Habits

which the study of it has a tendency to form.

—That the improvement of the power of

Reasoning ought to be regarded as only a

secondary Object in the culture of the Un-

derstanding, - - . 284

III.—In what respects the study of the Aristote-

lian Logic may be useful to Disputants.

—

A general acquaintance with it justly re-

garded as an essential accomplishment to

those who are liberally educated. ^—Doubts

3

xiv CONTENTS.

suggested by some late Writers, concerning

Aristotle's claims to the invention of the

Syllogistic Theory, - - Page 304

CHAP. I\^.

Of the MetJiod of Inquiry pointed out in the Experimental

or Inductive Logic.

Sect. I.—Mistakes of the Ancients concerning the proper

object of Philosophy.— Ideas of Bacon on

the same subject.—Inductive Reasoning.—A-

ualysis and Synthesis.—Essential difference

between Legitimate and Hypothetical Theo-

ries, _ - - 325

II.—Continuation of the Subject.—The Induction

of Aristotle compared with that of Bacon, 358

III.—Of the Import of the Words Analysis and Syn-

thesis in the Language of Modern Philoso-

phy, - - - - 373

I. Preliminary Observations on the Ana-

lysis and Synthesis of the Greek Geome-

tricians, - - 374

II. Critical Remarks on the vague Use, a-

mong Modern Writers, of the Terms

Analysis and Synthesis, - 386

IV.—The Consideration of the Inductive Logic re-

sumed, _ - - 404

I. Additional Remarks on the distinction

between Experience and Analogy.—Of

the grounds afforded by the latter for

Scientific Inference and Conjecture, ib,

II. Use and Abuse of Hypotheses in Philo-

sophical Inquiries.—Difference between

Gratuitous Hypotheses, and those which

are supported by presumptions suggest-

ed by Analogy Indirect Evidence

which a Hypothesis may derive from its

agreement with the Phenomena.—Cau-

tions against extending some of these

CONTENTS. XV

conclusions to the Philosophy of the

Human Mind, - Page 425

III. Supplemental Observations on the

Words Induction and Analogy, as used

in Mathematics, - - 431

Sect. V.—Of certain misapplications of the Words Expe-

rience and Induction in the phraseology of

Modern Science.—Illustrations from Medi-

cine and from Political Economy, - 459

VI.—Of the Speculation concerning Final Causes, 478

I. Opinion of Lord Bacon on the subject,

.^Final Causes rejected by Descartes,

and by the majority of French Philoso-

phers.—Recognised as legitimate Ob-

jects of research by Newton.—^Tacitly

acknowledged by all as a useful Logical

Guide, even in Sciences which have no

immediate relation to Theology, - ib.

II. Danger of confounding Final with Phy-

sical Causes in the Philosophy of the

Human Mind, - - 499

Conclusion of Part Second, - - 512

Notes and Illustrations, - - 523

Afpemdix, - - > . 583

ELEMENTS

PHILOSOPHY

OF THF,

HUMAN MIND.

PART SECOND,

OF REASON, OR THE UNDERSTANDING PROPERLY

SO CALLED ; AND THE VARIOUS FACULTIES AND

OPERATIONS MORE IMMEDIATELY CONNECTED

WITH IT.

PRELIMINARY OBSERVATIONS ON THE VAGUENESS

AND AMBIGUITY OF THE COMMON PHILOSOPHI-

CAL LANGUAGE RELATIVE TO THIS PART OF OUR

CONSTITUTION. REASON AND REASONING, UN-

DERSTANDING, INTELLECT, JUDGMENT, &C.

J HE power of Reason, of which I am now to treat,

is unquestionably the most important by far of those

which are comprehended under the general title of

Intellectual. It is on the right use of this power

that our success in the pursuit both of knowledge

VOL. II. A

Q ELEMENTS OF THE PHILOSOPHY

and of happiness depends ; and it is by the exclusive

possession of it that Man is distinguished, in the

most essential respects, from the lower animals. It

is, indeed, from their subsei'viency to its operations,

that the other faculties, which haye been hitherto

under our consideration, derive their chief value.

In proportion to the peculiar importance of this

subject are its extent and its difficulty ;—^both of

them such as to lay me under a necessity, now that I

am to enter on the discussion, to contract, in various

instances, those designs in wliich I was accustomed

to indulge myself, when I looked forward to it from

a distance. Tlie execution of them at present, even

if I were more competent to the task, appears to me,

on a closer examination, to be altogether incompati-

ble with the comprehensiveness of the general plan

which was sketched out in the advertisement prefix-

ed to the former volume ; and to the accomplish-

ment of which I am anxious, in the first instance, to

direct my efforts. If that undertaking should ever

be completed, I may perhaps be able afterwards to

offer additional illustrations of certain articles, which

the limits of this part of my work prevent me from

considering with the attention which they deserve.

I should wish, in particular, to contribute something

more than I can here introduce, towards a rational

and practical system of Logic, adapted to the present

state of human knowledge, and to the real business

of human life.

" AVhat subject," says Burke, " does not branch

*' out to infinity ! It is the nature of our particular

" scheme, and the single point of view in which we

OF THE HUMAN MIND. «^

** consider it, which ought to put a stop to our re-

" searches." * How forcibly does the remark apply

to all those speculations which relate to the prhici-

ples of the Human Mind !

I have frequently had occasion, in the course of

the foregoing disquisitions, to regret the obscurity in

which this department of philosophy is involved, by

the vagueness and ambiguity of words ; and I have

mentioned, at the same time, my unwillingness to at-

tempt verbal innovations, wherever I could possibly

avoid them, without essential injury to my argument.

The rule which I have adopted in my own practice

is, to give to every faculty and operation of the mind

its own appropriate name ; following, in the selec-

tion of this name, the prevalent use of our best

writers ; and endeaAôuring afterwards, as far as I

have been able, to employ each word exclusively in

that acceptation in which it has hitherto been used

most generally. In the judgments which I have

formed on points of this sort, it is more than probable

that I may sometimes have been mistaken ; but the

mistake is of little consequence, if I myself have in-

variably annexed the same meaning to the same

phrase ;—an accuracy which I am not so presump-

tuous as to imagine that I have uniformly attained,

but which I am conscious of having, at least, uni-

formly attempted. How far I have succeeded, they

alone who have followed my reasonings with a veiy

critical attention are qualified to determine ; for it

is not by the statement of formal definitions, but by

'-* Conclusion of the Inquiry into the Sublime and the Beautiful.

4 ELEMENTS OF THE PHILOSOPHY

the habitual use of precise and appropriate language,

that I have endeavoured to fix in my reader's mind

the exact import of my expressions.

In appropriating, however, particular words to par-

ticular ideas, I do not mean to censure the practice

of those who may have understood them in a sense

different from that which I annex to them ; but 1

found that, without such an appropriation, I could

not explain my notions respecting the human mind,

with any tolerable degree of distinctness. This

scrupulous appropriation of tenns, if it can be called

an innovation^ is the only one which I have attempt-

ed to introduce ; for in no instance have I presumed

to annex a philosophical meaning to a technical word

belonging to this branch of science, without having

previously shewn, that it has been used in the same

sense by good writers, in some passages of their works.

After doing this, I hope I shall not be accused of

affectation, when I decline to use it in any of the

other acceptations in which, from carelessness or from

want of precision, they may have been led occasion-

ally to employ it.

Some remarkable instances of vagueness and ambi-

guity, in the employment of words, occur in that

branch of my subject of which I am now to treat.

The word Reason itself is far from being precise in

its meaning. In common and popular discourse, it

denotes that power by which we distinguish truth

from falsehood, and right from wrong ; and by which

we are enabled to combine means for the attainment

of particular ends. Whether these different capaci-

ties are, with strict logical propriety, referred to the

OF THE HUMAN MIND. 5

same power, is a question which I shall examine manother part of my work ; but that they are all in-

cluded in the idea which is generally annexed to

the word reasoiiy there can be no doubt ; and the

case, so far as I know, is the same with the correspond-

ing terai in all languages whatever. The fact pro-

bably is, that this word was first employed to com-

prehend the principles, whatever they are, by which

man is distinguished from the brutes ; and after-

wards came to be somewhat limited in its meaning,

by the more obvious conclusions concerning the na^

ture of that distinction, which present themselves to

the common sense of mankind. It is in this en-

larged meaning that it is opposed to instinct by

Pope :

" And Reason raise o'er Instinct as you can;

" In this 'tis God directs, in that 'tis Man,"

It was thus, too, that Milton plainly understood

the term, when he remarked, that smiles imply the

exercise of reason

:

" Smiles from Reason flow,

" To brutes denied :"

And still more explicitly in these noble lines

:

" There wanted yet the master-work, the end

" Of ail yet done ; a creature who, not prone

" And brute as other creatures, but endued

" With sanctity of Reason, might erect

" His stature, and upright with front serene

" Govern the rest, self-knowing ; and from thence,

" Magnanimous, to correspond with Heaven

;

" But, grateful to acknowledge whence his good

" Descends, thither with heart, and voice, and eyes


" Direcled in devotion, to adore

" And worship God Supreme, who made him chief

" Of all his works."

Among the various characteristics of humanity,

the power of devising means to accomplish ends, to-

gether with the power of distinguishing truth from

falsehood, and right from wrong, are obviously the

most conspicuous and important ; and accordingly

it is to these that the word reason^ even in its most

comprehensive acceptation, is now exclusively re-

stricted.*

* This, I think, is the meaning which most naturally presents

itself to common readers, when the word reason occurs in authors

not affecting to aim at any nice logical distinctions ; and it is

certainly the meaning which must be annexed to it, in some of

the most serious and important arguments in which it has ever

been employed. In the toUowing passage, for example, where

Mr L;)cke contrasts the light of Reason wit^ that of Revelation,

he plainly Droceeds on the supposition, that it is competent to

appeal to the former, as affording a standard of right and wrong,

not less than of speculative truth and falsehood ; nor can there be

a doubt that, when he speaks of truth as the object of natural

reason, it was principally, if not wholly, moral truth which he

had in his view :'' Reason is natural revelation, whereby the

" eternal Father of Light, and fountaui of all knowledge, com-*' municates to mankmd that portion of truth which he has laid

" within the reach of their natural faculties. Revelation is natu-

" ral reason, enlarged by a new set of discoveries, communicated

" by (iod immediately, which reason vouches the truth of, by the

*' testimony and proofs it gives that they come from God. So** that he who takes away Reason to make way for Revelation, puts

" out the light of both, and does much the same as if he would

" persiiade a man to put out his eyes, the better to receive the

" remote light of an invisible star by a telescope,"—LocêV jEs-

say, B. iv. c. I9.


By some philosophers, the meaning of the word

has been, of late, restricted still farther ; to the

power by which we distinguish truth from falsehood,

and combine means for the accomplishment of our

purposes ;—the capacity of distinguishing right from

wrong, being referred to a separate principle or

faculty, to which different names have been assigned

in different ethical theories. The following passage

from Mr Hume contains one of the most explicit

statements of this limitation which I can recollect

:

" Thus, the distinct boundaries and offices of reason

" and of taste are easily ascertained. The former

" conveys the knowledge of truth and falsehood ;

" the latter gives the sentiment of beauty and defor-

*' mity,—vice and virtue. Reason, being cool and" disengaged, is no motive to action, and directs only

*' the impulse received from appetite or inclination,

" by shewing us the means of attaining happiness or

" avoiding misery. Taste, as it gives pleasure or

** pain, and thereby constitutes happiness or misery,

A passage still more explicit for my present purpose occurs in

the pleasing and philosophical conjectures of Huyghens, concern-

ing the planetary worlds. " Positis vero ejusmodi planetaruni

" incolis ratione utentibus, quaeri adhuc potest, anne idem illic,

" atque apud nos, sit hoc quod rationan vocamus. Quod quidem

" ita esse omnino dicendum videtur, neque aliter lieri posse ; sive

" usum rationis in his consideremus quae ad mores et afequitatem

" pertinent, sive in iis quae spcctant ad principia ct fundamenta

" scientiarum. Etenim ratio apud nos est, quae sensuin justitice,

" honesti, laudis, clementiae, gratitudinis ingenerat, mala ac bona

" in universum discernere docet : quaequead hajc animum disci-

" plinae, multorumque inventorum capacem reddit,'' &c. &c.—

«

Hugenii Opera Varia, Vol. II. p. 663. Lugd. Batav. 1724.

8 ELEMENTS OP THE PHILOSOPHY

" becomes a motive to action, and is the first spring

" or impulse to desire and volition.*'*

On the justness of this statement of Mr Hume,

I have no remarks to offer here ; as my sole object

in quoting it was to illustrate the different meanings

annexed to the word reaso7i by different writers.

It will appear afterwards, that, in consequence of

this circumstance, some controversies, which have

been keenly agitated about the principles of morals,

resolve entirely into verbal disputes ; or, at most,

mto questions of arrangement and classification, of

little comparative moment to the points at issue, t

Another ambiguity in the Word reason, it is of

still greater consequence to point out at present;

an ambiguity which leads us to confound our ration-

* Essays and Treatises, &c. Appendix, concerning Moral

Sentiment.

\ In cenfirmation of this remark, T shall only quote at present

a few sentences from an excellent discourse, by Dr Adams of

Oxford, on the nature and obligations of virtue. " Nothing can

" bring us under an obligation to do what appears to our moral

"judgment wrong. It may be supposed our interest to do this;

*' but it cannot be supposed our duty. Power may compel,

" interest may bribe, pleasure may persuade ; but reason only

" can oblige. This is the only authority which rational beings

" can own, and to which they owe obedience."

It must appear perfectly obvious to every reader, that the ap-

parent difference of opinion between this writer and Mr Hume

turns chiefly on the different degrees of latitude with which they

have used the word reason. Of the two, there cannot be a doubt

that Dr Adams has adhered by far the most faithfully, not only

to its acceptation in the works of our best English authors, but

to the acceptation of the corresponding term in the ancient

languages. " Est quidem vera lex, recta ratio- quae vocet

" ad officium, jubendo; vetando, a fraude deterreat," &c. &c>

OF THE HUMAN MIND. ^

fil powers in general with that particular branch of

them, known among logicians by the name of the

Discursivefaculty. The affinity between the words

reason and reasoning sufficiently accounts for this

inaccuracy in common and popular language ; al-

though it cannot fail to appear obvious, on the

slightest reflection, that, in strict propriety, reason-

ing only expresses one of the various functions or

operations of reason ; and that an extraordinary ca-

pacity for the former by no means affi)rds a test by

which the other constituent elements of the latter

may be measured. * Nor is it to common and po-

pular language that this inaccuracy is confined. It

has extended itself to the systems of some of our

most acute philosophers, and has, in various in-

stances, produced an apparent diversity of opinion

where there was little or none in reality.

" No hypothesis," says Dr Campbell, *' hitherto

*' invented, hath shewn that, by means of the discur-

" sive faculty, without the aid of any other mental

" power, we could ever obtain a notion of either

" the beautiful or the good." t The remark is un-

doubtedly true, and may be applied to all those

systems which ascribe to Reason the origin of our

moral ideas, if the expressions reason and discur-

sivefaculty be used as synonymous. But it was as-

suredly not in this restricted acceptation, that the

word reason was understood by those ethical writers

* " The two most different things in the world," siiys Locke,

" are, a logical chicaner, and a man of reason."

—

Conduct of the

Understandings § 3.

+ Philosophy of Rhetoric, Vol. I. p. 204.


at whose doctrines this criticism seems to have been

pointed by the ingenious author. That the discur-

sive faculty alone is sufficient to account for the ori-

gin of our moral ideas, I do not know that any theo-

rist, ancient or modem, has yet ventured to assert.

Various other philosophical disputes might be

mentioned, which would be at once brought to a

conclusion, if this distinction between reason and

the power of reasoning were steadily kept in view.. *

* It is curious, that Dr Johnson has assigned to this very li-

mited, and (according to present usage) very doubtful interpreta-

tion of the word reason, the Jii'st place in his enumeration of its

various meanings, as if he had thought it the sense in which it is

most properly and correctl)' employed. " Reason,'' he tells us,

" is the power by which man deduces one proposition from an-*' other, or proceeds from premises to consequences." The

authority which he has quoted for this definition is still more cu-

rious, being manifestly altogether inapplicable to his purpose.

" Reason is the director of man's will, discovenng in action what

" is good; for the laws of well-doing are the dictates of right

" reason.''

—

Hooker.

In the sixth article of the same enumeration, he states, as a

distinct meaning of the same word, ratiocination, discursive 'power..

What possible difference could he conceive between this signifi-

cation and that above quoted ? The authority, however, which

he produces for this last explanation is worth transcribing. It is

a passage from Sir John Davis, where that fanciful writer states

a distinction between reason and understanding, to which be

seems to have been led by a conceit founded on their respective

etymologies.

" WIrfn she rates things, and moves from ground to ground,

" Tlie name of Re:ison she obtains by this;

*' Hnt whfn by R>âson she the truth hath found,

" r'Mul .sla Mleih lixt, she Uiiderslamiing is."

The adjective reasonable, as employed m our language, is not

liable to the same ambiguity with the substantive from which it is

10

OP THE HUMAN MIND, 11

In the use which I make of the word reaso7i, in

the title of the following disquisitions, I employ it

in a manner to which no philosopher can object

—

to denote merely the power by which we distin-

guish truth from falsehood, and combine means for

the attainment of our ends : omitting, for the pre-

sent, all consideration of that function which many

have ascribed to it, of distinguishing right from

wrong ; without, however, . presuming to call in

question the accuracy of those by whom the term

has been thus explained. Under the title of Rea-

son^ I shall consider also whatever faculties and

operations appear to be more immediately and es-

sentially connected with the discovery of truth, or

the attainment of the objects of our pursuit,—more

particularly the Power of Reasoning or Deduction;

but distinguishing, as carefully as I can, our capa-

city of carrying on this logical process, from those

derived. It denotes a character in which reason (taking that

word in its largest acceptation) possesses a decided ascendant

over the temper and the passions ; and implies no particidar pro-

pensity to a display of the discursive power, if, indeed, it does

not exclude the idea of such a propensity. In the following

stanza. Pope certainly had no view to the logical talents of the

lady whom he celebrates :

" I know a thing that's most uncommon," (Envy be silent and attend)

" I know a reasonable m oman,

" Handsome and witty, yet a friend."

Of this reasonable woman, we may venture to conjecture, with

some confidence, that she did not belong to the class of those

femmes raisonnemes, so happily described by Moliere :

" Raisonner est Temploi de tonte ma maison

" Et ie raisonneuiGut en bannit la raisoii."


more comprehensive powers which Reason is under-

stood to imply.

The latitude with which this word has been so

universally used, seemed to recommend it as a con-

venient one for a general title, of which the object

is rather comprehension than precision. In the dis-

cussion of particular questions, I shall avoid the em-

ployment of it as far as I am able ; and shall endea-

vour to select other modes of speaking, more exclu-

sively significant ofthe ideas which I wish to convey.*

* Mr Locke too has prefixed the same title, Of Reason, to the

17th chapter of his Fourth Book, using the word in a sense near-

ly coinciding with that very extensive one which I wish my read-

ers to annex to^t here.

After observing, that by reason he means " that faculty vvhere-

" by man is supposed to be distinguished from brutes, and where-

*' in it is evident he much surpasses them ;" he adds, that " we" may in reason consider these four degrees ;—the first and high-

" est is the discovering and finding out of proofs ; the second,

" the regular and methodical disposition of them, and laying

*' them in a clear and fit order, to make their connection and

" force be plainly and easily perceived ; the third is the perceiv-

" ing their connection ; and the fourth is making a right con-

" elusion."

Dr Reid's authority for this use of the word is equally exnli-

cit: " The power of reasoning is very nearly allied to that of

judging. We include both under the name of reason."—Intel,

led. Powers, p. 67 1, 4to edit.

Another authority to the same purpose is furnished by Milton:

-" Whence the soul

" Reason receives ; and Rtason is her being—' —Discursive or intuitive." Par. Lost, B. v. 1. 4SG.

I presume that Milton, who was a logician as well as a poet,

means by the words her being, her essential or characteristical

endowment.


Another instance of the vagueness and indistinct-

ness of the common language of logicians, in treat-

ing of this part of the Philosophy of the HumanMind, occurs in the word U7iderstanding. In its

popular sense, it seems to be very nearly synony-

mous with reason^ when that word is used most

comprehensively ; and is seldom or never applied

to any of our faculties, but such as are immediately

subservient to the investigation of truth, or to the

regulation of our conduct. In this sense, it is so

far from being understood to comprehend the powers

of Imagination, Fancy, and Wit, that it is often

stated in direct opposition to them ; as in the com-

mon maxim, that a sound understanding and a

warm imagination are seldom united in the same

person. But philosophers, without rejecting this

use of the word, very generally employ it, with far

greater latitude, to comprehend all the powers which

I have enumerated under the title of Intellectual

;

referring to it Imagination, Memory, and Percep-

tion, as well as the faculties to which it is appro-

priated in popular discourse, and which it seems in-

deed most properly to denote. It is in this manner

that it is used by Mr Locke in his celebrated Es-

To these quotations I shall only add a sentence from a rery

judicious French writer, which I am tempted to introduce

here, less on account of the sanction which it gives to my own

phraseology, than of the importance of the truth which it con-

veys,

" Reason is commonly employed as an instrument to acquire

" the sciences ; wliereas, on the contrary, the sciences ought to

" be made u.>e of a- an instrument to give reason its perfection."

-îjArt ae Penser, translated by Ozeil, p. 2. London, 1717.

14> ELEMENTS OF THE PHILOSOPHY

say ; and by all tlie logicians who follow the com-

mon division of our mental powers into those of the

Understanding and those of the Will.

In mentioning this ambiguity, I do not mean to

cavil at the phraseology of the writers from whom it

has derived its origin, but only to point it out as a

circumstance which may deserve attention in some

of our future disquisitions. The division of our

powers which has led to so extraordinary an exten-

sion of the usual meaning of language, has an ob-

vious foundation in the constitution of our nature,

and furnishes an arrangement which seems indis-

pensable for an accurate examination of the subject

:

nor was it unnatural to bestow on those faculties,

which are all subservient in one way or another to

the right exercise of the Understanding, the name

of that power, from their relation to which their

chief value arises.

As the word understanding, however, is one of

those which occur very frequently in philosophical

arguments, it may be of some use to disengage it

from the ambiguity just remarked ; and it is on this

account that I have followed the example of some

late writers, in distinguishing the two classes of

powers which were formerly referred to the Under-

standing and to the Will, by calling the former in-

tellectualy and the latter active. The terms cogni-

tive and motive were long ago proposed for the

same purpose by Hobbes ; but they never appear to

have come into general use, and are indeed liable to

obvious objections.

It has probably been owing to the very compre-


henslve meaning annexed in philosophical treatises

to the word Understandings that the use of it has

so frequently been supplied of late by Intellect,

The two words, as they are commonly employed,

seem to be very nearly, if not exactly, synonymous ;

and the latter possesses the advantage of being quite

unequivocal, having never acquired that latitude of

application of which the fonner admits. The ad-

jective intellectual indeed, has had its meaning ex-

tended as far as the substantive understandi7ig

;

but, as it can be easily dispensed with in our parti-

cular arguments, it may, without inconvenience, be

adopted as a distinctive epithet, where nothing is

aimed at but to mark, in simple and concise lan-

guage, a very general and obvious classification.

The word intellect can be of no essential use what-

ever, if the ambiguity in the signification of the

good old English word understanding be avoided;

and as to intellection^ which a late very acute writer *

has attempted to introduce, I can see no advantage

attending it, which at all compensates for the addi-

tion of a new and uncouth term to a phraseology

which, even in its most simple and unaffected form,

is so apt to revolt the generality of readers.

The only other indefinite word which I shall

take notice of in these introductory remarks \^judg-

ment ; and, in doing so, I shall confine myself to

such of its ambiguities as are more peculiarly con-

nected with our present subject. In some cases,

its meaning seems to approach to that of under-

* Dr Campbell. Sec his Philosophy of Rhetoric, Vol. I.

p. 103, 1st edit.


Standing ; as in the nearly synonymous phrases, a

sound understanding, and a soundjudgment. If

there be any difference between these two modes of

expression, it appears to me to consist chiefly in

this, that the former implies a greater degree of po-

sitive ability than the latter ; which indicates rather

an exem})tion from those biasses which lead the

mind astray, than the possession of any uncommon

reach of capacity. To understanding we apply the

epithets strong, vigorous, comprehensive, profound :

To judg7nent, those of correct, cool, unprejudiced,

impartial, solid. It was in this sense that the word

seems to have been understood by Pope, in the fol-

lowing couplet

:

" 'Tis with our judgments as our watches ; none

*' Go just alike, yet each believes his own."

For this meaning of the word, its primitive and

literal application to the judicial decision of a tribu-

nal accounts sufficiently.

Agreeably to the same fundamental idea, .the

name o^judgment i^ given, with peculiar propriety,

to those acquired powers ofdiscernment which charac-

terize a skilful critic in the fine arts;powers which

depend, in a very great degree, on a temper of

mind free from the undue influence of authority and

of casual associations. The power of Taste itself

is frequently denoted by the appellation oi judg-

ment ; and a person who possesses a more than ordi-

nary share of it is said to be ajudge in those matters

which fall under its cognizance.

The meaning annexed to the word by logical

7


writers is considerably different from this ; denoting

one of the simplest acts or operations of which we

are conscious, in the exercise of our rational powers.

In this acceptation, it does not admit of definition,

any more than semation, mlly or belief. All that

can be done, in such cases, is to describe the occasions

on which the operation takes place, so as to direct

the attention of others to their own thoughts. With

this view, it may be observed, in the present instance,

that when we give our assent to a mathematical

axiom ; or when, after perusing the demonstration

of a theorem, we assent to the conclusion ; or, in

general, when we pronounce concerning the truth or

falsity of any proposition, or the probability or impro-

bability of any event, the power by which we are

enabled to perceive what is true or false, probable or

improbable, is called by logicians the faculty ofjudg-

Tuent. The same word, too, is frequently used to

express the particular acts of this power, as when the

decision of the understanding on any question is

called a judgment of the mind.

In treatises of logic, judgment is commonly de-

fined to be an act of the mind, by which one thing

is affirmed or denied of another ; a definition which,

though not unexceptionable, is perhaps less so than

most that have been given on similar occasions. Its

defect (as Dr Reid has remarked) consists in this,

—

that, although it be by affirmation or denial that we

express our judgments to others, yet judgment is a

solitary act of the mind, to which this affiimation or

denial is not essential ; and, therefore, if the defini-

VOL. II. B


tion be admitted, it must be understood of mental

affimiation or denial only ; in wliicli case, we do no

more than substitute, instead of tlie thing defined,

another mode of speaking perfectly synonymous.

The definition has, however, notwithstanding this

imperfection, the merit of a conciseness and per-

spicuity, not often to l)e found in the attempts of

logicians to explain our intellectual operations.

Mr Locke seems disposed to restrict the word

judgjnent to that faculty which pronounces concern-

ing the verisimilitude of doubtful propositions ; em-

ploying the word knowledge to express the faculty

which perceives the truth of propositions, either in-

tuitively or demonstratively certain. ** The faculty

** which God has given man to supply the want of

" clear and certain knorwledge^ in cases where that

*' cannot be had, {^judgment ; whereby the mind** takes its ideas to agree or disagree ; or, which is

" the same thing, any proposition to be true or false,

" without perceiving a demonstrative evidence in the

" proofs.

*' Thus, the mind has t^ faculties, conversant

" about truth and falsehood.

** First, knowledge, whereby it certainly perceives,

** and is undoubtedly satisfied of the agreement or

" disagreement of any ideas.

" êcowdXj,judgment, which is the putting ideas

*' together, or separating them from one another in

" the mind, when their agreement or disagreement

** is not perceived, but presumed to be so ; which is,

** as the word imports, taken to be so, before it

" certainly appears. And if it so unites or separates

OF THE HUI^TAN MIND. 19

" them, as in reality tilings are, it is right judg-*' 77ie?it.*'

*

For this limitation in the definition of jiidgmenf,

some pretence is afforded by the literal signification

of the word, when applied to the decision of a tribu-

nal ; and also, by its metaphorical application to the

decisions of the mind, on those critical questions

whicli fall under the province of Taste. But, con-

sidered as a technical or scientific term of Logic, the

practice of our purest and most correct writers suf-

ficiently sanctions the more enlarged sense in which

I have explained it ; and, if I do not much deceive

myself, this use of it will be found more favourable

to philosophical distinctness than Mr Locke's lan-

guage, which leads to an unnecessaiy multiplication

of our intellectual powers. What good reason can

be given for assigning one name to the faculty which

perceives truths that are certain, and another name

to the faculty which perceives truths that ar^ pro-

bable ? Would it not be equally proper to distin-

guish, by different names, the power by which weperceive one proposition to be true, and another to

h^false ?

As to hnoxvledge, I do not think that it can, with

propriety, be contrasted with judgment ; nor do I

apprehend that it is at all agreeable, either to com-

mon use or to philosophical accuracy, to speak of

knowledge as ^Jaculti/, To me it seems rather to

denote the possession of those truths about which

our faculties have been previously employed, than.

* Essay on the Human Uiulerstajiding, Book iv. chap. 14.


any separate power of the understanding, by which

truth is perceived.*

* In attempting thus to fix the logical import of various

words in our language, which are apt to be "confounded, in popu-

lar speech, with reason, and also with reasoiwig, some of myreaders may be surprised, tliat I have said nothing about the

word •uiisdom. The truth is, that the notion expressed by this

term, as it is employed by our best writers, seems to presuppose

the influence of some principles, the consideration of which be-

longs to a different part of my work. In confirmation of this,

it may be remarked, that whereas the province of our reasoning

powers (in their application to the business of life), is limited to

the choice of means, wisdom denotes a power of a more compre-

hensive nature, and of a higher order ; a power which implies a

judicious selection both of means and of ends. It is very precise-

ly defined by Sir William Temple, to be " that which makes

" men judge what are the best ends, and what the best means to

** attain them."

Of these two modifications of wisdom, the one denotes a power

of the mind which obviously falls under the view of the logician

;

the examination of the other, as obviously, belongs to ethics.

A distinction similar to this was plainly in the mind of Cud-

worth when he wrote the following passage, which, although

drawn from the purest sources of ancient philosophy, will, I doubt

not, from the uncouthness of the phraseology, have the appear-

ance of extravagance to many in the present times. To myself

it appears to point at afact of the highest importance in the mo-

ral constitution of man.

** We have all of us by nature //ai/TSu/i/st ji (as both Plato and

" Aristotle call it) a certain divination, presage, and parturieiit

" vaticination in our minds, of some higher good and perfection,

" than either power or knowledge. Knowledge is plainly to be.

" preferred before power, as being that which guides and directs

" its blind force and impetus; but Aristotle himself declares,

" that there is Koy^ rt nfiiTTov, which is hoya tfp^w > something

" better than reason and knowledge, which is the principle and ori»

" gmal oj it. For (saith he) hoy>i a.^yyi a Kaytî, aKKcl xi


Before concluding these preliminary remarks, I

cannot help expressing my regret, that the subject

on which I am about to enter will so frequently lay

me under the necessity of criticising the language,

and of disputing the opinions of my predecessors.

In doing so, I am not conscious of being at all in-

fluenced by a wish to indulge myself in the cap-

tiousness of controversy ; nor am I much afraid of

this imputation from any of my readers who shall

honour these speculations with an attentive perusal.

My real aim is, in the ^rst place, to explain the

grounds of my own deviations from the track which

has been commonly pursued ; and, secondly^ to fa-

cilitate the progress of such as may follow me in the

same path, by directing their attention to those

points of divergency in the way, which may suggest

matter for doubt or hesitation. I know, at the same

time, that, in the opinion of many, the best mode of

unfolding the principles of a science is to state them

systematically and concisely, without any historical

retrospects whatever ; and I believe the opinion is

well-founded, in those departments of knowledge,

" KfiiiTTOv- The principle of reason is not reason, but something

" better."—Intellectual System, p. 203.

Lord Sliaftesbury has expressed the same truth more simply

and perspicuously in that beautiful sentence which occurs more

than once in his writings :" True wisdom comes more from

" the heart than from the head,"—Numberless illustrations of

this profound maxim must immediately crowd on the memory

of all who are conversant with the most enlightened works on

the theory of legislation ; more particularly with those which

appeared, during the eighteenth century, on the science of poli-

tical economy:

^^. ELEMENTS OF THE PHILOSOPHY

wliere tlie difficulty arises less from vague ideas and

indefinite terms, than from the length of the logi-

cal chain which the student has to trace. But, in

such disquisitions as we are now engaged in, it is

chiefly from the gradual correction of verbal ambi-

guities, and the gradual detection of unsuspected

prejudices, that a progressive, though slow approxi-

mation to truth is to be expected. It is indeed a

slow approximation, at best, that we can hope to ac-

complish at present, in the examination of a subject

where so many powerful causes (particularly those

connected with the imperfections of language) con-

spire to lead us astray. But the study of the hu-

man mind is not, on that account, to be abandoned.

Whoever compares its actual state with that in

which Bacon, Descartes, and Locke found it, must

be sensible how amply their efforts for its improve-

ment have been repaid, both by their own attain-

ments, and by those of others who have since pro-

fited by their example. I am willing to hope, that

soine useful hints for its farther advancement maybe derived even from my own researches ; and, dis-

tant as the prospect may be of raising it to a level

with the physical science of the Newtonian school,

by uniting the opinions of speculative men about

fundamental principles, my ambition as an author

will be fully gratified, if, by the few who are com-

petent to judge, I shall be allowed to have contri-

buted my share, however small, towards the attain-

ment of so great an object.

In the discussions which immediately follow, no

argument will, I trust, occur beyond the reach of

OF THE HUMAN MIND. SS

those who shall read them with the attention which

every inquiry into the human Mind indispensably

requires. I have certainly endeavoured, to the ut*

most of my abilities, to render every sentence whicli

I have written, not only intelligible but perspicuous j

and, where I have failed in the attempt, the obscu-

rity will, I hope, be imputed, not to an affectation

of mystery, but to some error of judgment. I can,

without much vanity, say, that, with less expence of

thought, I could have rivalled the obscurity of

Kant ; and that the invention of a new technical

language, such as that which he has introduced,

would have been an easier task, than the communi-

cation of clear and precise notions (if I have been

so fortunate as to succeed in this connnunication),

without departing from the established modes of

expression.

To the following observations of D*Alembert

(with some trifling verbal exceptions) I give mymost cordial assent ; and, mortifying as they may

appear to the pretensions of bolder theorists, I

should be happy to see them generally recognised as

canons of philosophical criticism : " Truth in meta-

" physics resembles truth in matters of taste. In

" both cases, the seeds of it exist in every mindj

" though few think of attending to this latent trea-

" sure, till it be pointed out to them by more cu-

" rious inquirers. It sliould seem that everything

" we learn from a good metaphysical book is only a

** sort of reminiscence of what the mind previously

" knew. The obscurity, of which we are apt to

" complain in this science, may be always justly as-

24f ELEMENTS OF THE PHILOSOPHY

** cribed to the autlior ; because the infonnation

" which he professes to communicate requires no*' technical language appropriated to itself. Ac-" cordingly, we may apply to good metaphysical

" authors what has been said of those who excel in

" the art of writing, that, in reading them, every-

" body is apt to imagine that he himself could

*' have written in the same manner.

" But, in this sort of speculation, if all are quali-

" fied to understand, all are not fitted to teach.

" The merit of accommodating easily to the appre-

" hension of others, notions which are at once simple

" and just, appears, from its extreme rarity, to be

" much greater than is commonly imagined. Sound" metaphysical principles are truths which every one

" is ready to seize, but which few men have the

" talent of unfolding ; so difficult is it in this, as

" well as in other instances, to appropriate to one's

" self what seems to be the common inheritance of

" the human race."*

I am, at the same time, fully aware, that whoever,

* " Le vrai en metaphysique ressemble au vrai en inalicVe de

" gofit ; c'est un vrai dont tous Ics espiils ont le germe en eux-

" memes, auquel la plupart no font point d'attention, mais qu'ils

*' reconnoissent dcis qu'on le leur monlrc. U semble que tout ce

" qu'on apprend dans un bon livie de metaphysique, ne soit

*' qu'une espece de reminiscence de ce que notre ame a deja su;

" I'obscurite, quand il y en a, vjent toujours de la laule de I'au-

" teur, parce que la science qu'il se propose d'enseigner n'a point

*' d'autre langue que la langue commune. Aussi peut-on appli.

" quer aux bons auteurs de metaphysique ce qu'on a dit des bons

" ecrivains, qu'il n'y a personne qui en Ics lisant, ne croie pou-

*' voir en dire autant qu'eux.

OF THE HUMAN MIND. S5

111 treating of the Human Mind, aims to be under-

stood, must lay his account with forfeiting, in the

opinion of a very large proportion of readers, all pre-

tensions to depth, to subtlety, or to invention. The

acquisition of a new nomenclature is, in itself, no in-

considerable reward to the industry of those, who

study only from motives of literary vanity ; and, if

D'Alembert's idea of this branch of science be just,

the wider an author deviates from truth, the more

likely are his conclusions to assume the appearance

of discoveries. I may add, that it is chiefly in those

discussions which possess the best claims to origi-

nality, where he may expect to be told by the multi-

tude, that they have learned from him nothing but

what they knew before.

The latitude with which the word metaphysics

is frequently used, makes it necessary for me to re-

jnark, with respect to the fox'egoing passage from

D*Alembert, that he limits the term entirely to an

account of the origin of our ideas. " The genera-

" tion of our ideas," he tells us, "belongs to meta-

** physics. It forms one of the principal objects,

** and perhaps ought to form the sole object of that

" Mais si dans ce genre tous sont fails pour entendre, tons ne

'* sont pas faits pour instruire. Le merite de faire entrer avec

'• facilite dans les esprits des notions vraies et simples, est beau-

" coup plus grand qu'on ne pense, puisque I'experience nous

" prouve combien il est rare ; les saines idees metaphysiques

" sont des veriles communes que chacun saisit, mais que pcu

" d'hommes ont le talent de developper ; tant il est difficile, dans

" quelque sujet que ce puisse etre, de se rend re propre ce qui ap.

" partieut a tout ie monde."

—

Elemens dc Philosophies

g6 ELEMENTS OF THE PHILOSOPHY

" science."*—If the meaning of the word be extend-

ed, as it too often is in our language, so as to com-

prehend all those inquiries which relate to the theory

and to the improvement of our mental powers, some

of his observations must be understood with very

important restrictions. What he has stated, how-

ever, on the inseparable connection between perspi-

cuity of style and soundness of investigation in me-

taphysical disquisitions, will be found to hold equally

in every research to which that epithet can, with any

colour of propriety, be applied.

* " La generation de nosidees appartieiit h la metaphyîque;

""c'est un de ses objets principaux, et peut-etre devroit elle s'y

" borner,"—Ibid.

Chap. I. OF THE HUMAN MIND. Tl

CHAPTER FIRST.

OF THE FUNDAMENTAL LAWS OF HUMAN BELIEF

;

OR THE PRIMARY ELEMENTS OF HUMAN REASON.

1 HE propriety of tlie title prefixed to this Chapter

will, I trust, be justified suflSciently by the specula-

tions which are to follow. As these differ, in some

essential points, from the conclusions of former writ-

ers, I found myself under the necessity of abandon-

ing, in various instances, their phraseology ;—^but

my reasons for the particular changes which I have

made, cannot possibly be judged of, or even under-

stood, till the inquiries by which I was led to adopt

them be carefully examined.

I begin with a review of some of those primary

truths, a conviction of which is necessarily implied in

all our thoughts and in all our actions, and which

seem, on that account, rather to form constituent and

essential elements of reason, than objects with which

reason is conversant. The import of this last remark

will appear more clearly afterwards.

The primary truths to which I mean to confine

my attention at present are, 1 . Mathematical Axioms

:

2. Truths (or, more properly speaking, Laws of

Belief), inseparably connected with the exercise of

Consciousness, Perception, Memoiy, and Reason-

28 ELEMENTS OF THE PHILOSOPHY Chap. I.

ing.—Of some additional laws of Belief, the truth

of which is tacitly recognised in all our reasonings

concerning contingent events, I shall have occasion

to take notice under a different article.

Section I.

Of Mathematical Axioms.

I HAVE placed this class of truths at the head of

the enumeration, merely because they seem likely,

from the place which they hold in the elements of

geometiy, to present to my readers a more interest-

ing, and, at the same time, an easier subject of discus-

sion, than some of the more abstract and latent ele-

ments of our knowledge, afterwards to be consider-

ed. In other respects, a different arrangement

might perhaps have possessed some advantages, in

point of strict logical method.

I.

On the evidence of mathematical axioms it is un-

necessary to enlarge, as the controversies to which

they have given occasion are entirely ofa speculative,

or rather scholastic description ; and have no ten-

dency to affect the certainty ofthat branch of science

to which they are supposed to be subservient.

It must, at the same time, be confessed, with

respect to this class of propositions (and the same re-

mark may be extended to axioms in general), that

some of the logical questions connected with them

continue still to be involved in much obscurity. In

proportion to their extreme simplicity is the diffi-

10

Sect. 1. OF THE HUMAN MIND. SQ

culty of Illustrating or of describing their nature in

unexceptionable language ; or even of ascertaining a

precise criterion by which they may be distinguished

from other truths which approach to them nearly.

It is chiefly owing to this, that, in geometry, there

are no theorems of wliich it is so difficult to give a

rigorous demonstration, as those, of which persons,

unacquainted with the nature of mathematical evi-

dence, are apt to say, that they require no proof

whatever. But the inconveniences arising from

these circumstances are of trifling moment ; occasion-

ing, at the worst, some embarrassment to those

mathematical writers, who are studious of the most

finished elegance in their exposition of elementary

principles ; or to metaphysicians, anxious to dis-

play their subtilty upon points which cannot possi-

bly lead to any practical conclusion.

It was long ago remarked by Locke, of the axi-

oms of geometry, as stated by Euclid, that although

the proposition be at first enunciated in general

terms, and afterwards appealed to, in its particular

applications, as a principle previously examined and

admitted, yet that the truth is not less evident in the

latter case than in the former. He observes farther,

that it is in some of its particular applications, that

the truth of every axiom is originally perceived by

the mind ; and, therefore, that the general proposi-

tion, so far from being the ground of our assent to

the truths which it comprehends, is only a verbal

generalization of what, in particular instances, has

been already acknowledged as true.

The same author remarks, that some of these axi-

30 ELEMENTS OF THE PHILOSOPHY Chap. I,

cms " are no more than bare verbal proix)sItions,

" and teach us nothing but the respect and import

" of names one to another. The 'ivhole is equal to

" all its jyarts : what real truth, I beseech you, does

" it teach us ? What more is contained in that max-** im, than what the signification of the word totum,

*' or the U'/toley does of itself import ? And he that

" knows that the word tvhole stands for what is

" made up of all its parts, knows very little less,

" than that ' the whole is equal to all its parts.'

" And upon the same ground, I think, that this pro-

" position, A hill is higher than a valley^ and se-

" veral the like, may also pass for maxims."

Notwithstanding these considerations, Mr Locke

does not object to the form which Euclid has given

to his axioms, or to the place which he has assigned

to them in his Elements. On the contrary, he is of

opinion, that a collection of such maxims is not with-

out reason prefixed to a mathematical system ; in

order that learners, " having in the beginning per-

** fectly acquainted their thoughts with these pro-

** positions made in general tei-ms, may have them** ready to apply to all particular cases as formed

" rules and sayings. Not that, if they be equally

" weighed, they are more clear and evident than

" the instances they are brought to confirai ; but

" that, being more familiar to the mind, the very

" naming of them is enough to satisfy the under-

** standing.^" In farther illustration of this, he adds,

very justly and ingeniously, that, " although our

" knowledge begins in particulars, and so spreads

" itself by degrees to generalsj

yet, afterwards, the

Sfect. 1. O*" THE HUMAN MIND. 31

•* mind takes quite the contrary course, and having

** drawn its knowledge into as general propositions

** as it can, makes them familiar to its thoughts, and

" accustoms itself to have recourse to them, as to the

** standards of truth and falsehood.'*

But although, in mathematics, some advantage

may be gained, without the risk of any possible in-

convenience, from this arrangement of axioms, it is

a very dangerous example to be followed in ether

branches of knowledge, where our notions are not

equally clear and precise ; and where the force of

our pretended axioms (to use Mr Locke's words),

" reaching only to the sound, and not to the signi-

" fication of the words, serves only to lead us into

<* confusion, mistakes, and error." For the illus-

tration of this remark, I must refer to Locke.

Another observation of this profound writer de-

serves our attention, while examining the nature of

axioms ;—" that they are not the foundations on

" which any of the sciences is built ; nor at all iise-

" ful in helping men forward to the discovery of un-

" known truths." * This observation I intend to

illustrate afterwards, in treating of the futility of the

syllogistic art. At present I shall only add, to what

Mr Locke has so well stated, that, even in mathe-

matics, it cannot with any propriety be said, that the

axioms are the foundation on which the science rests;

or the first principles from which its more recondite

truths are deduced. Of this I have little doubt that

Locke was perfectly aware j but the mistakes wliich

* Book iy. chap. f. § H % 3.


some of the most acute and enlightened of his dis-

ciples have committed in treating of the same sub-

ject, convince me, that a further elucidation of it is

not altogether superfluous. With this view, I shall

here introduce a few remarks on a passage in DrCampbell's Philosophy of Rhetoric, in which he has

betrayed some misapprehensions on this very point,

which a little more attention to the hints already

quoted from the Essay on Human Understanding

might have prevented. These remarks will, I hope,

contribute to place the nature of axioms, more par-

ticularly of mathematical axioms, in a different and

clearer light than that in which they have been com-

monly considered.

" Of intuitive evidence," says Dr Campbell,

*' that of the following propositions may serve as an

" illustration : One and four make five. Things

*' equal to the same thing are equal to one another.

" The whole is greater than a part ; and, in brief,

" all axioms in arithmetic and geometry. These** are, in effect, but so many expositions of our

" own general notions, taken in different views.

" Some of them are no more than definitions, or

*' equivalent to definitions. To say, one and four

" make jive^ is precisely the same thing as to

"say, we give the name o^ Jive to one added to

** four. In fact, they are all in some respects re-

" ducible to this axiom, whatever is, is. I do not

" say they are deduced from it, for they have in

*' like manner that original and intrinsic evidence,

" which makes them, as soon as the terms are un-

" derstood, to be perceived intuitively. And, if

Sect. 1. OF THE HUMAN MIND. 33

** they are not thus perceived, no deduction of reason

** vNill ever confer on them any additional evidence.

" Nay, in point of time, the discovery of the less

** general truths has the priority, not from their su-

** perior evidence, but solely from this consideration,

" that the less general are sooner objects of percep-

" tion to us. But I affirm, that though not deduced

" from that axiom, they may be considered as par-

** ticular exemplifications of it, and coincident with

" it, inasmuch as they are all implied in this, that

" the properties of our clear and adequate ideas can

" be no other than what the mind clearly perceives

* them to be.

" But, in order to prevent mistakes, it will be

** necessary further to illustrate this subject. It

" might be thought that, if axioms were propositions

" perfectly identical, it would be im])ossible to ad-

" vance a step, by their means, beyond the simple

" ideas first perceived by the mind. And it must

" be owned, if the predicate of the proposition were

" nothing but a repetition of the subject, under the

** same aspect, and in the same or synonymous terms,

" no conceivable advantage could be made of it for

" the furtherance of knowledge. Of such proposi-

" tions, for instance, as these,—seven are seven,

*' eight are eight, and ten added to eleven are equal

" to ten added to eleven, it is manifest that we could

" never avail ourselves for the improvement of

" science. Nor does the change of the term make" any alteration in point of utility. The proposi-

** tions, twelve are a dozen, twenty are a score, un-

VOL. II. c

34« ELEMENTS OP THE PHILOSOPHY Chap. I.

*' less considered as explications of the words dozen** and score, are equally insignificant with the for-

" mer. But when the thing, though in effect coin-

" ciding, is considered under a different aspect

;

** when what is single in the subject is divided in the

" predicate, and conversely ; or when what is a

" whole in the one is regarded as a part of some-

*' thing else in the other ; such propositions lead to

" the discoveiy of innumerable and apparently re-

" mote relations. One added to four may be ac-

*' counted no other than a definition of the word" five, as was remarked above. But when I say,

" * Two added to three are equal to five,' I advance

" a truth which, though equally clear, is quite dis-

" tinct from the preceding. Thus, if one should

" affirm, * That twice fifteen make thirty,* and" again, that ' thirteen added to seventeen make" thirty,' nobody would pretend that he had repeat-

" ed the same proposition in other words. The" cases are entirely similar. In both cases, the

" same thing is predicated of ideas which, taken se-

" verally, are different. From these again result

** other equations, as ' one added to four are equal

" to two added to three,* and ' twice fifteen are

" equal to thirteen added to seventeen.*

" Now, it is by the aid of such simple and ele-

" mentary principles, that the arithmetician and al-

" gebraist proceed to the most astonishing discove-

" ries. Nor are the operations of the geometrician

" essentially different."

I have little to object to these observations of DrCampbell, as far as they relate to arithmetic and to

Sect. I. OF THE HUMAN MIND. S5

algebra ; for, in these sciences, all our investigations

amount to notliing more than to a comparison of

different expressions of the same thing. Our com-

mon language, indeed, frequently supposes the case

to be otherwise ; as when an equation is defined to

be, "A proposition asserting the equality of two

*' quantities.'* It would, however, be nuich more

correct to define it, *' A proposition asserting the

" equivalence of two expressions of the same quan-

** tity ;'* for algebra is merely a universal arithme-

tic ; and the names of numbers are nothing else

than collectives, by which we are enabled to express

ourselves more concisely than could be done by enu-

merating all the units that they contain. Of this

doctrine, the passage now quoted from Dr Camp-

bell shews that he entertained a sufficiently just and

precise idea.

But, if Dr Campbell perceived that arithmetical

equations, such as " one and four make five," ai-e

no other than definitions, why should he have class-

ed them with the axioms he quotes from Euclid,

*' That the whole is greater than a part," and that

" Things equal to the same thing are equal to one

" another ;"—propositions which, however clearly

their truth be implied in the meaning of the terms

of which they consist, cannot certainly, by any inter-

pretation, be considered in the light of definitions

at all analogous to the former ? The former, indeed,

are only explanations of the relative import of par-

ticular names ; the latter are universal propositions,

applicable alike to an infinite variety of instances. *

* D'-Alembert also has confounded the^ctwo classc? of propo-


Another very obvious consideration might have

satisfied Dr Campbell, tliat the simple arithmetical

equations which he mentions, do not hold tlie same

place in that science which Euclid's axioms hold in

geometry. What I allude to is, that the greater

part of these axioms are equally essential to all the

different branches of mathematics. That " the

" whole is greater than a part," and that *' things

*' equal to the same thing are equal to one another,**

are propositions as essentially connected with our

ârithmetical computations, as with our geometrical

reasonings ; and, therefore, to explain in what man-

ner the mind makes a transition, in the case of

numbers, from the more simple to the more compli-

sitions. " What do the greater part of those axioms on which

" geometfy prides itself amount to, but to an expression, by

*' means of two dift'erent words or signs, of the same simple

*' idea ? He who says that two and two make four, what more

" does he know than another who should content himself with

" saying, that two and two make two and two ?" Here, a

simple arithmetical equation (which is obviously a mere dejini.

turn) is brought to illustrate a remark on the nature of geometri-

cal axioms. With respect to these last (I mean such axioms

as Euclid has prefixed to his Elements), D'Alembert's opinion

seems to coincide exactly with that of Locke, already mentioned.

" 1 would not be understood, nevertheless, to condemn the use

" of them altogether: 1 wish only to remark, that their utility

" rises no higher than this, that they render our simple ideas

" more familiar by means of habit, and better adapted to the dif«

*' ferent purposes to which we may have occasion to apply

" them."—" Je ne pretends point cependant en condamner ab-

" solunient I'usage : je veux seulement faire observer, a quoi il se

" reduit; c'est a nous rendre les idees simples plus familieres par

" I'habitude, et plus propres aux difiercns usages auxquels nous

*' pouvons les appliquer."

—

DiscoufS Piiiiminaire, &c, 6^0.

Sect. K OF THE HUMAN MIND. &J

cated equations, throws no light whatever, on the

question, hoxv the transition is made, either in

arithmetic or in geometry, from what are properly

called axioms, to the more remote conclusions in

these sciences.

The very fruitless attempt thus made by this

acute writer to illustrate the importance of axioms

as the basis of mathematical truth, was probably

suggested to him by a doctrine which has been re-

peatedly inculcated of late, concerning the grounds

of that peculiar evidence which is allowed to accom-

pany mathematical demonstration. " All the

' sciences (it has been said) rest ultimately on first

* principles, which we must take for granted with-

' out proof; and whose evidence determines, both

' in kind and degree, the evidence which it is pos-

' sible to attain in our conclusions. In some of

' the sciences, our first principles are intuitively

' certain ; in others, they are intuitively probable ;

* and such as the evidence of these principles is,

' such must that of our conclusions be. If our

' first principles are intuitively certain, and if we' reason from them consequentially, our conclusions

* will be demonstratively certain : but if our prin-

' ciples be only intuitively probable, our conclu-

* sions will be only demonstratively probable. In

* mathematics, the first principles from which we' reason are a set of axioms which are not only in-

' tuitively certain, but of which we find it impos-

' sible to conceive the contraries to be true : And* hence the peculiar evidence which belongs to all

38 ELEMENTS OF THE PHILOSOPHY C'ha|). I.

" the conclusions that follow from these principles

" as necessary consequences.'*

To this view of the subject Dr Reid has repeat-

edly given his sanction, at least in the most essen-

tial points ; more particularly, in controverting an

assertion of Locke's, that ** no science is, or hath

" been built on maxims.*'—'* Surely," says Dr Reid,

** Mr Locke was not ignorant of geometiy, which

" hath been built upon maxims prefixed to the Ele-

" ments, as far back as we are able to trace it. But

" though they had not been prefixed, which was a

" matter of utility rather than necessity, yet it must

" be granted, that eveiy demonstration in geometry

*' is grounded, either upon propositions formerly

" demonstrated, or upon self-evident principles." *

On another occasion he expresses himself thus :

" I take it to be certain, that whatever can, by just

*' reasoning, be infeiTed from a principle that is ne-

" cessary, must be a necessary truth. Thus, as the

** axioms in mathematics are all necessary truths,

" so are all the conclusions drawn from them ; that

" is, the whole body of that science." t

That there is something fundamentally erroneous

in these very strong statements with respect to the

relation which Euclid's axioms bear to the geome-

trical theorems which follow, appears sufficiently

from a consideration which was long ago mention-

ed by Locke,—that from these axioms it is not pos-

sible for human ingenuity to deduce a single infer-

* Essays on Intell. Powers, p. 647, 4to edit.

T Ibid. p. 577* See also pp. 56'0, 56l, 606\

Sect. I. OF THE HUMAN MIND. 39

ence. " It was not," says Locke, " the influence

** of those maxims which are taken for principles in

" mathematics, that hath led the masters of that

" science into those wonderful discoveries they have

** made. Let a man of good parts know all the

" maxims generally made use of in mathematics,

*' never so perfectly, and contemplate their extent

** and consequences as much as he pleases, he will,

" by their assistance, I suppose, scarce ever come to

" know, that * the square of the hypothenuse in a

" right angled triangle, is equal to the squares of

" the two other sides.' The knowledge that * the

*' whole is equal to all its parts,* and, ' if you take

*' equals from equals, the remainders will be equal,*

** helped him not, I presume, to this demonstra-

" tion : And a man may, I think, pore long enough

" on those axioms, without ever seeing one jot the

** more of mathematical truths.*' * But surely, if

this be granted, and if, at the same time, by the

first principles of a science be meant those funda-

mental propositions from which its remoter truths

are derived, the axioms cannot, with any consis-

tency, be called the First Principles of Mathema-

tics. They have not (it will be admitted) the most

distant analogy to what are called the first prin-

ciples of Natural Philosophy ;—to those general

facts, for example, of the gravity and elasticity of

the air, from which may be deduced, as conse-

quences, the suspension of the mercury in the Tor-

ricellian tube, and its fall when carried up to an

* Essay on Human Understanding, Book IV. chap. xii. ^15.

40 ELEMENTS OF THE PHILOSOPHY Chap, t

eminence. According to this meaning of the wordy

the principles of mathematical science are, 7iot the

axioms, but the definitions ; which definitions hold,

m mathematics, precisely the same place that is

held in natural philosophy by such general facts as

have now been referred to.*

From what principle are the various properties of

* In order to prevent cavil, it may be necessary for me to re-

mark here, that, when I speak of mathematical axioms, I have in

view only such as are of the same description with ih.ejirst nint

of those which are prefixed to the Elements of Euclid ; for, in

ikmt list, it is well known, that there are several which belong to

a class of propositions altogether different from the others. That

"all right angles (for example) are equal to one another;'*

that " when one straight line falling on two other straight lines

" makes the two interior angles on the same side leas than two*' right angles, these two straight lines, if produced, shall meet" on the side, where are the two angles less than two right

" angks ;" are manifestly principles which bear no analogy to

such barren truisms as these, " Things that are equal to one and

" the same thing are equal to one another." " If equals be ad-

" ded to equals, the wholes are e(|ual." " If equals be taken from

" equals, the remainders are equal." Of these propositions, the

two former (the 10th and 11th axioms, to wit, in Euclid's list)

are evidently theorems which, in point of strict logical accuracy,

ought to be demonstrated ; as may be easily done, with respect

to the first, in a single sentence. That the second has not yet

been proved in a simple and satisfactory manner, has been long

considered as a sort of reproach to mathematicians ; and I have

little doubt that this reproach will continue to exist, till the

basis of the science be somewhat enlarged, by the introduction,

of one or two new definitions, to serve as additional principles of

geometrical reasoning.

For some farther remarks on Euclid's Axioms, see Note (A.)

The edition of Euclid to which I uniformly refer, is that ef

David Gregory. Oxon. I7i3.

Sect. 1» OF THE HUMAN MIND. 41

the circle derived, but from the definition of a

circle ? From what principle the properties of the

parabola or ellipse, but from the definitions of these

curves ? A similar observation may be extended to

all the other theorems which the mathematician de-

monstrates : And it is this observation (which, ob-

vious as it may seem, does not appear to have oc-

curred, in all its force, either to Locke, to Reid, or

to Campbell) that furnishes, if I mistake not, the

true explanation of the peculiarity already remarked

in mathematical evidence.*

Tlie prosecution of this last idea properly belongs

to the subject of mathematical demonstration, of

which I intend to treat afterwards. In the mean-

time, I trust that enough has been said ô correct

those misapprehensions of the nature of axioms,

which are countenanced by the speculations, and

still more by the phraseology, of some late eminent

writers. On this article, my own opinion coincides

very nearly with that of Mr Locke—both in the

view which he has given of the nature and use of

* D'Alcmbcrt, although he sometimes seems to speak a dif-

ferent language, approached nearly to this view of the subject

when he wrote the following passage :

*' Finally, it is not without reason that mathematicians con-

" sider dejinitions as principles ; since it is on clear and precise

" definitions that our knowledge rests in those sciences, where

" our reasoning powers have the widest field opened for their ex-

" ercise."—" An rcste, ce n'est pas sans raison que les mathe-

" maticiens regardent les definitions comme des principes, pu-*• isque, dans les sciences ou le raisonnement a la meillure part,

" c'est sur des definitions nettes et exactesque nos-connoissances

" sent appuyees."-—Eltmens de Phil. p. 4.


axioms in geometry, and in what he has so forcibly

urged concerning the danger, in other branches of

knowledge, of attempting a similar list of mai'ims,

without a due regard to the circumstances by which

different sciences are distinguished from one another.

With Mr Locke, too, I must beg leave to guard

myself against the possibility of being misunder-

stood in the illustrations which I have offered of

some of his ideas : And for this purpose, I cannot

do better than borrow his words. " In all that is

*' here suggested concerning the little use of axioms

" for the improvement of knowledge, or dangerous

" use in undetermined ideas, I have been far enough** from saying or intending they should be laid aside,

" as some have been too forward to charge me. I

" affirm them to be truths, self-evident truths ; and

" so cannot be laid aside. As far as their influence

" will reach, it is in vain to endeavour, nor would I

*' attempt to abridge it. But yet, without any in-

" jury to truth or knowledge, I may have reason to

" think their use is not answerable to the great

'* stress which seems to be laid on them, and I may'* warn men not to make an ill use of them, for the

" confirming themselves in error."*

After what has been just stated, it is scarcely

necessary for me again to repeat, with regard to

mathematical axioms, that although they are not the

principles of our reasoning, either in arithmetic or

in geometry, their truth is supposed or implied in

all our reasonings in both ; and, if it were called in

question, our further progress would be impossible.

* Locke's Essay, Book iV. ch, vii. § 14.


In both of these respects, we shall find them analo-

gous to the other classes of primary or elemental

truths which remam to be considered.

Nor let it be imagined, from this concession, that

the dispute turns merely on the meaning annexed

to the word priiiciple. It turns upon an important

question of fact -, Whether the theorems of geome-

try rest on the axioms, in the same sense in which

they rest on the definitions ? or (to state the ques-

tion in a manner still more obvious). Whether

axioms hold a place in geometry at all analogous to

what is occupied in natural philosophy, by those

sensible phenomena which form the basis of that sci-

ence ? Dr Reid compares them sometimes to the

one set of propositions and sometimes to the other.*

If the foregoing observations be just, they bear no

analogy to either.

Into this indistinctness of language Dr Reid was

* '* Matliematics, once fairly established on the foundation of

" a few axioms and definitionsy as upon a rock, has grown from

" age to age, so as to become the loftiest and the most solid fa.

" brie that human reason can boast."

—

Essays on Int. Powers,

p. 561, 4to edition.

** Lord Bacon first delineated the only solid foundation on

" which natural philosophy can be built ; and Sir Isaac Newton" reduced the principles laid down by Bacon into three or four

" axioms, which he calls regidce philosophandi. From these, to-

" gether with the phenomena observed by the senses, 'which he likC"

" wise lays down as Jirst principles, he deduces, by strict reason-

" ing, the propositions contained in the third book of his Princi-

" pia, and in his Optics ; and by this means has raised a fabric,

" which is not liable to be shaken by doubtful disputation, but

" stands immoveable on the basis of self-evident principles."—

Ibid. See also pp. 647, 648,

4f4t ELEMENTS OP THE PHILOSOPHY Chap. I.

probably led in part by Sir Isaac Newton, who, with

a very illogical latitude in the use of words, gave

the name of axioms to the laxcs of motio7i, * and

also to those general experimental truths which form

the ground-work of our general reasonings in catop-

trics and dioptrics. For such a misapplication of

the technical terms of mathematics some apology

might perhaps be made, if the author had been treat-

ing on any subject connected with moral science

;

but surely in a work entitled " Mathematical Princi-

* Axiomata, sive leges Motus. Vide Phitosophice Naturalis

Frincipia Mathematka.

At the beginning, too, of Newton's Optics, the title of axioms

is given to the following propositions :

*' Axiom I.

" The angles of reflection and refraction lie in one and the

" same plane with the angle of incidence.

*' Axiom II.

" The angle of reflection is equal to the angle of incidence.

" Axiom III.

" If the refracted ray be turned directly back to the point of

•' incidence, it shall be refracted into the line before described by

" the incident ray.

*' Axiom IV.

" Refraction out of the rarer medium into the denser, is made

** towards the perpendicular ; that is, so that the angle of refrac-

" tion be less than the angle of incidence.

" Axiom V,

" The sine of incidence is either accurately, or very nearly in

** a given ratio to the sine of refraction."

When the word axiom is understood by one writer in the sense

annexed to it by Euclid, and by his antagonist in the sense here

given to it by Sir Isaac Newton, it is not surprising that there

should be apparently a wide diversity between their opinions con-

cerning the logical importance of this class of propositions.


" pies of Natural Philosophy,'* the word aîom

might reasonably have been expected to be used in

a sense somewhat analogous to that which every

person liberally educated is accustomed to annex to

it, when he is first initiated into the elements of

geometry.

The question to which the preceding discussion

relates is of the greater consequence, that the pre-

vailing mistake with respect to tlie nature of mathe-

matical axioms, has contributed much to the support

of a very erroneous theory concerning mathematical

evidence, which is, I believe, pretty generally adopt-

ed at present,—that it all resolves ultimately into

the perception of identity ; and that it is this cir-

cumstance which constitutes the peculiar and cha-

racteristical cogency of mathematical demonstration.

Of some of the other arguments which have been

alleged in favour of this theory, I shall afterwards

have occasion to take notice. At present, it is suf-

ficient for me to remark (and this I flatter myself

I may venture to do with some confidence, after the

foregoing reasonings), that in so far as it rests on

the supposition that all geometrical tmths are ulti-

mately derived from Euclid's axioms, it proceeds on

an assumption totally unfounded in fact, and indeed

so obviously false, that nothing but its antiquity can

account for the facility with which it continues to be

admitted by the learned. *

* A late mathematiciarit of considerable ingenuity and learn-

ing, doubtful, it should seem, whether Euclid had laid a suffi-

ciently broad foundation for mathematical" science in the axioms

prefixed to his Elements, has thought proper to introduce several


II.

Continuation of the same Subject,

The difference of opinion between Locke and

Reid, of which I took notice in the foregoing part

of this Section, appears greater than it really is, in

consequence of an ambiguity in the word principle,

as employed by the latter. In its proper accepta-

tion, it seems to me to denote an assumption (whe-

ther resting on fact or on hypothesis), upon which,

as a datum^ a train of reasoning proceeds ; and for

the falsity or incorrectness of which no logical rigour

in the subsequent process can compensate. Thus

the gravity and the elasticity of the air are principles

ofreasoning in our speculations about the barome-

ter. The equality of the angles of incidence and re-

flection ; the proportionality of the sines of incidence

new ones of his own iuvention. The first of these is, that " Every

" quantity is equal to itself ;" to which he adds afterwards, that

" a quantity expressed one way is equal to itself expressed any

" other way."

—

See Elements of Mathematkal xinalysis, by PrO'

^^fessor Vilant of St Andrews. We<ire apt to smile at the for-

mal statement of these propositions ; and yet, according to th«i

theory alluded to in the text, it is in truths of this very descrip-

tion that the whole science of rcathcmatics not only begins but

ends. '' Omnes mathematicoruni propositiones sunt idcnticjB, et

*' repraesentantur hac formula, a z=. a." This sentence, which

I quote from a dissertation published at Berlin about fifty years

ago, expresses, in a few words, what seems to be now the pre-

vailing opinion (more particularly on the Continent) concerning

the nature of mathematical evidence. The remarks which I have

to offer upon it I delay till some other questions sh .H be previ-

ously considered, ?

Sect. 1. OF THE HUMAN.MIND. 47

and refraction ; are principles ofreasoning in catop-

trics and in dioptrics. In a sense perfectly analo-

gous to this, the definitions of geometry (all of

which are merely hypothetical) are the Jirst princi-

ples of reasoning in the subsequent demonstrations,

and the basis on which the whole fabric of the science

rests.

I have called this the proper acceptation of the

word, because it is that in which it is most frequent-

ly used by the best wa-iters. It is also most agreeable

to the literal meaning which its etymology suggests,

expressing the original point from which our reason-

ing sets out or commences.

Dr Reid often uses the word in this sense, as, for

example, in the following sentence, already quoted :

" From three or four axioms, which he calls regulw

" philosophandi^ together with the phenomena oh-

" served by the senses^ which he likewise lays down" as Jirst 'principles^ Newton deduces, by strict rea-

" soning, the propositions contained in the third

" book of his Principia, and in his Optics.'*

On other occasions, he uses the same word to de-

note those elemental truths (if I may use the expres-

sion) which are virtually taken for granted or as-

sumed, in every step of our reasoning ; and without

which, although no consequences can be directly in-

ferred from them, a train of reasoning would be im-

possible. Of this kind, in mathematics, are the «^'-

ioms, or (as Mr Locke and others frequently call

them) the maxims ; in physics, a belief of the con-

tinuance of the Laws of Nature ;—in all our rea-

sonings, without exception, a belief in our own


identity, and in the evidence of memory. Such

truths are the last elements into which reasoning re-

solves itself, when subjected to a metaphysical ana-

lysis ; and which no person but a metaphysician or

a logician ever thinks of stating in the form of pro-

positions, or even of expressing verbally to himself.

It is to truths of this description that Locke seems

in general to apply the name of maHms ; and, in

this sense, it is unquestionably true, that no science

(not even geometry) is founded on maxims as its first

principles.

In one sense of the word principle, indeed, max-

ims may be called principles of reasoning ; for the

words principles and elements are sometimes used

as synonymous. Nor do I take upon me to say that

this mode of speaking is exceptionable. All that I

assert is, that they cannot be called principles qfreasoning, in the sense which has just now been de-

fined ; and that accuracy requires, that the word,

en which the whole question hinges, should not be

used in both senses, in the course of the same argu-

ment. It is for this reason that I have employed

the phrase principles ofreasoning on the one occa-

sion, and elements ofreasoning on the other.

It is difficult to find unexceptionable language to

mark distinctions so completely foreign to the ordi-

nary purposes of speech ; but, in the present in-

stance, the line of separation is strongly and clearly

drawn by this criterion,—that from princijjles of

reasoning consequences may be deduced ; from what

I have called elements qf reasonings none ever can.

A process of logical reaspnin"; has been often


likened to a chain supporting a weight. If this si-

militude be adopted, the axioms or ele^nental truths

now mentioned may be compared to the successive

concatenations which connect the different links im-

mediately with each other ; the principles of our

reasoning resemble the hook, or rather the beam,

from which the whole is suspended.

The foregoing observations, I am inclined to

think, coincide with what was, at bottom, Mr Locke's

opinion on this subject. That he has not stated it

with his usual clearness and distinctness, it is impos-

sible to deny ; at the same time, I cannot subscribe

to the following severe criticism of Dr Reid :

'* Mr Locke has observed, ' That intuitive know-** ledge is necessary to connect all the steps of a de-

** monstration.*

" From this, I think, it necessarily follows, that

" in every branch of knowledge, we must make use

*' of trutlis that are intuitively known, in order to

** deducefrom them such as require proof.

*' But I cannot reconcile this with what he says

** (section 8th of the same chapter) : * The necessity

" of this intuitive knowledge in every step of scien-

*^ tifical or demonstrative reasoning, gave occasion,

*' I imagine, to that mistaken axiom, that all reason-

" ing was ex pt^wcognitis et pr^wconcessis, which*' how far it is mistaken I shall have occasion to

" shew more at large when I come to consider

" propositions, and particularly those propositions

*' which are called maxims, and to shew that it

"is by a mistake that they are supposed to be

VOL. II. D

•50 ELEMENTS OF TME PHILOSOPHY C\M\[y. I.

** the foundation of all oiu* knowledge and reason-

" inffs."*

The distinction which 1 liave already made be-

tween elements of reasoning, and ^/irst principles of

reasoning, appears to myself" to throw much light on

these apparent contradictions.

That the seeming difference of opinion on this

point between these two profound writers, arose

chiefly from the ambiguities of language, may be in-

ferred from the following acknowledgment of DrReid, which immediately follows the last quotation :

*' I liave carefully examined the chapter on max-" ims, which Mr Locke here refers to, and though*' one would expect, from the quotation last made," that it should run contrary to what I have before

*' delivered concerning first principles, I find only

*' two or three sentences in it, and those chiefly in-

^' cidentul, to which I do not assent." t

Before dismissing this subject, I must once more

repeat, tliat the doctrine which I have been attempt-

ing to establish, so far from degrading aaioms from

that rank which Dr Reid would assign them, tends

to identify them still more than he has done with

the exercise of our reasoning powers ; inasmuch as,

instead of comparing them with the data, on the ac-

curacy of which that of our conclusion necessarily

depends, it considers them as the vincula w hich give

coherence to all the particular links of the chain ;

or (to vary the metaphor) as component elementSj

* Essays on Int. Powers, p. 64:3, 4to edit.

f Ibid.

Sect. 1

.

OF THE HUMAN MIND. <51

,

without which the faculty of reasoning is inconceiv-

able and impossible. *

* D'Alembert has defined the word principle cxatlly in the

sense in which I have used it ; and has expressed hirnseli (at

least on one occasion) nearly as 1 have done, on the subject of

axioms. He seems, however, on this, as well as on some other

logical and metaphysical questions, to have varied a little in his

views (probably from mere forgetfulness) in different parts of his

writings.

" >Vhat then are the truths which are entitled to have a place

" in the elements of philosophy ? They are of two kinds ; t/iosc

" whichform the head of each part of the chain, and those whicli

" are to be lound at the points where different branches of the

" chain unite t;)gether.

" Truths of the first kind are distinguished by this— that ihcy

" do not depend on any other truths, and that they possess with-

" in themselves the whole grounds of their evidence. Some oi

" my readers will be apt to suppose, that I here mean to speak of

" axioms; but these are not the truths which I have at present

" in view. With respect to this last class of principles, I must

" refer to what I have elsewhere said of them ; that, notwithstand-

*' ing their truth, they add nothing to our information ; and that

" the palpable evidence which accompanies them, amounts to no-

" thing more than to an expression of the same idea by means ot

" two different terms. On such occasions, the mind only turns

" to no purpose about its own axis, without advancing forward a

" single step. Accordingly, axioms are so far from holding th(-

** highest rank in philosophy, that they scarcely deserve the dis-

" tinction of being formally enunciated."

*' Or quelles sont Ics verites qui doivcnt entrer dans des e'.e •

" mens de philosophie? II y en a de deux sortes; celles qui fur-

" ment la tete de chaque partie de la chaine, et celles qui se trouvent

*' au point de reunion de plusieurs branches.

'' Les verites du premier genre ont pour caract^re dislinctif de

" ne dependre d'aucune autre, et de n'avoir de preuves que dans

" elles.memes. Plusieurs lecteurs croiront que nous voulons par-

'* ler dcs axioms^ et i!s se tromperont ; nous les rcnvoyons ii gc qui

52 ELEMENTS OF THE PHILOSOPHY Chap, I.

Section II.

Of certain Laws of Belief inseparably connected

with the exercise ofConsciousnesSy Memory^ Per-

ceptiony and Reaso7iing.

1. It is by the immediate evidence of conscious-

ness that we are assured of the present existence of

" nous en avons dit ailleurs, que ces sortes de principes ne nous

" apprenhent rien a force d'etre vrais, ct que leur evidence pal-

" pable et grossiere se reduit a exprimer la meme idee par deux

" termts differens, I'esprit ne fait alors autre chose que tourner iii-

" utilement sur lui-meme sans avancer d'un seul pas. Ainsi les

" axioms, bien loin de teiiir en philosophiele premier rang, n'ont

" pas meme besoin d'etre enonces."

—

Elim, de Phil. pp. 24, 25.

Although, in the foregoing passage, D'Alembert, in compli-

ance with common phraseology, has bestowed the name o{ prin-

ciples upon axioms, it appears clearly, from a question which oc-

curs afterwards, that he did not consider them as well entitled to

this appellation. " What are then," he asks, " in each science, the

'* true principles from which we ought to set out?" (" Quels sont

" done dans chaque science les vrais priiicipes d'ou I'on doit par-

" tir?") The answer he gives to this question agrees with the

doctrine I base slated in every particular, excepting in this, that

it represents (and in my opinion very incorrectly) the principles

«f geometrical science to be (not defmitions or hypotheses, but)

those simple and acknowledged facts, which our senses perceive

with respect to the \no^ciiiG% oi extension. *' 'We true principles

" from which we ought to set out in the different sciences, are

" simple and acknowledged facts, which do not presuppose the

" existence of any others, and which, of course, it is equally vain

" to attempt explaining or confuting ; in physics, the familiar

" phenomena which daily experience presents to every eye; in

' geometri/, the sensible properties of extension; in mechanics, the

" impenetrability of bodies, upon which their mutual actions de>

pend ; in nietaphys-ics, the results of our sensations ; in mo-

S«ct. «. OF THE HUMAN MIND. 5S

our various sensations, whether pleasant or painful

;

of all our affections, passions, hopes, fears, desires,

and volitions. It is thus, too, we are assured of the

present existence of those thoughts which, during

our waking hours, are continually passing through

the mind, and of all the different effects which they

produce in furnishing employment to our intellec-

tual faculties.

According to the common doctrine of our best

philosophers, * it is by the evidence of conscious-

ness we are assured that we ourselves exist. The

proposition, however, when thus stated, is not ac-

curately true ; for our own existence (as I have

elsewhere observed) t is not a direct or immediate

object of consciousness, in the strict and logical

meaning of that term. We are conscious of sensa-

tion, thought, desire, volition ; but we are not con-

scious of the existence of Mind itself ; nor would it

" rals, the original and common aflfeciions of the human race."

—^" Les vrais principcs d'ou Ton doit partir dans chaque science,

" sont des faits simples et reconnus, qui n'en supposent point

" d'autres, et qu'on ne puisse par consequent ni expliquer ni con-

" tester ; en physique les phenomenes journaliers que I'observa-

*' tion d^couvre k tons les yeux ; eii geometric les proprietes sen-

*' sibles de Fetendue ; en mechanique, I'impenetrabilite des corps,

*' source de leur action mutuelle ; en metaphysique, le resultat

" de nos sensations ; en morale, les affections premieres et com-

" munes a tous les hommes." pp. 26, 27-

In cases of this sort, where so much depends on extreme preci-

sion and nicety in the use of words, it appears to me to be proper

to verify the fidelity of my translations by subjoining the original

passages.

* See, in particular, Campbell's Philosophy of Rhetoric.

+ Philosophical Essays, 4to edit. p. 7.

54 ELEMENTS OF THE PHILOSOPHY Chap. I,

be possible for us to arrive at the knowledge of it

(supjiosing us to be created in the full possession of

all the intellectual capacities which belong to hu-

man natm'e), if no impression were ever to be madeon our external senses. The moment that, in con-

sequence of such an impression, a sensation is ex-

cited, we learn two facts at once ;—the existence of

the sensation, and our own existence as sentient

beings ;—in other words, the very first exercise of

consciousness necessarily implies a belief, not only

of the present existence of what is felt, but of the

present existence of that vvhich feels and thinks;

or (to employ plainer language) the present exist-

ence of that being which I denote by the words /and myself. Of these facts, however, it is the for-

mer alone of which we can properly be said to be

conscious, agreeably to the rigorous interpretation

of the expression. A con^^ction of the latter, al-

though it seems to be so inseparable from the exer-

cise of consciousness, that it can scarcely be consi-

dered as posterior to it in the order of fmiCi is yet

(if I may be allowed to make use of a scholastic dis-

tinction) posterior to it in the order of nature ; not

only as it supposes consciousness to be already

awakened by some sensation, or some other mental

affection ; but as it is evidently rather a judgment

accompanying the exercise of that power, than one

of its immediate intimations concerning its appro-

priate class of internal phenomena. It appears to

me, therefore, more correct to call the belief of our

own existence a concomitant or accessoiy of the

.exercise of consciousness, than to say, that our exist-j


ence is a fact falling under the immediate cogniz-

ance of consciousness^ like the existence of the va-

rious agreeable or painful sensations which external

objects excite in our minds.

2. That we cannot, without a very blameable la-

titude in the use of words, be said to be conscious

of our personal identity, is a proposition still more

indisputable ; inasmuch as the very idea of personal

identity involves the idea of timey and consequently

presupposes the exercise not only of co?iscioiiS7iess,

but ©f memory. The belief connected with this

idea is implied in every thought and every action q^

the mind, and may l>e justly regarded as one of .the

simplest and most essential elements of the under-

standing. Indeed, it is impossible to conceive either

an intellectual or an active being to exist without it.

It is, however, extremely worthy of remark, with

respect to this belief, that, universal as it is among

our species, nobody but a metaphysician ever thinks

of expressing it in words, or of reducing into the

shape of a proposition the truth to which it relates.

To the rest of mankind, it forms not an object of

knowledge ; but a condition or supposition, neces-

sarily and unconsciously involved in the exercise

of all their faculties. On a part of our constitu-

tion, wiiich is obviously one of the last or primor-

dial elements at which it is possible to arrive in

analyzing our intellectual operations, it is plainly

unphilosophical to suppose, that any new light can

be thrown by metaphysical discussion. All that

can be done with propriety, in such cases, is to state

the fact.

56 ELEMENTS OP THE PHILOSOPHY Chap. I.

And here, I cannot help taking notice of the ab-

surd and inconsistent attempts which some inge-

nious men have made, to explain the gradual pro-

cess by which they suppose the mind to be led to

the knowledge of its own existence, and of that

continued identity which our constitution leads us

to ascribe to it. How (it has been asked) does a

child come to form the very abstract and metaphy-

sical idea expressed by the pronoun / or mot ? In

answer to this question, I have only to observe, that

when we set about the explanation of a pheno-

menon, we must proceed on the supposition that it

is possible to resolve it into some more general law

or laws with which we are already acquainted. But,

in the case before us, how can this be expected, by

those who consider that all our knowledge of mind

is derived from the exercise of reflection ; and that

eveiy act of this power implies a conviction of our

own existence as reflecting and intelligent beings ?

Every theory, therefore, which pretends to account

for this conviction, must necessarily involve that sort

of paralogism which logicians call apetitio principti

;

inasmuch as it must resolve the thing to be explain-

ed into some law or laws, the evidence of which rests

ultimately on the assumption in question. From

this assumption, which is necessarily implieftl in the

joint exercise of consciousness and memory, the phi-

losophy of the human mind, if we mean to study it

analytically, must of necessity set out ; and the very

attempt to dig deeper for its foundation, betrays a

total ignorance of the logical rules, according to

which alone it can ever be prosecuted with any hopes

of success.

Sect 2. OF THE HUMAN MIND. 57

It was, I believe, first remarked by M. Prevost of

Geneva (and the remark, obvious as it may appear,

reflects much honour on his acuteness and sagacity),

that the inquiries concerning the mind, founded on

the hypothesis of the animated statue—inquiries

which both Bonnet and Condillac professed to carry

on analytically,—were in truth altogether syntheti-

cal. To this criticism it may be added, that their

inquiries, in so far as they had for their object to ex-

plain the origin of our belief of our own existence,

and of our personal identity, assumed, as the prin-

ciples of their synthesis, facts at once less certain

and less familiar than the problem which they were

employed to resolve.

Nor is it to the metaphysician only that the ideas

of identity and of personality are familiar. Where

is the individual who has not experienced their

powerful influence over his imagination, while he was

employed in reflecting on the train of events which

have filled up the past history of his life ; and on

that internal world, the phenomena of which have

been exposed to his own inspection alone ? On such

an occasion, even the wonders of external nature

seem comparatively insignificant ; and one is tempt-

ed (with a celebrated French writer), in contemplat-

ing the spectacle of the Universe, to adopt the words

of the Doge of Genoa, when he visited Versailles

—

*' Ce qui m'etonne le plus ici, c*est de m'y voir." *

3. The belief which all men entertain of the ex-

istence of the material world (I mean their belief

* D'Alembert, Apologia de I'Etude.

58 ELEMENTS OF THE PHILOSOPHY Chap. L

of its existence independently of that of percipient

beings), and their expectation of the continued iini-

formity of the laws of nature, belong to the same

class of ultimate or elemental laws of thought, with

those which have been just mentioned. The truths

which form their objects are of an order so radically

different from v^hat are commonly called truthsy in

the popular acceptation of that word, that it might

perhaps be useful for logicians to distinguish them

by some appropriate appellation, such, for example,

as that of metaphysical or transcendental truths.

They are not |>r/?ic//?/e5 or data (as will afterwards

appear) from which any consequence can be de-

duced ; but form a part of those original stamina of

human reason, which are equally essential to all the

pursuits of science, and to all the active concerns of

life,

4. I shall only take notice farther, under this

head, of the confidence which we must necessarily

repose in the evidence of memory (and, I may add,

in the continuance of our personal identity), when

we are employed in carrying on any process of de-

duction or argumentation ;—in following out, for in-

stance, the steps of a long mathematical demonstra-

tion. In yielding our assent to the conclusion to

which such a demonstration leads, we evidently

trust to the fidelity with which our memory has

connected the different links of the. chain together.

The reference which is often made, in the course of

a demonstration, to propositions fonnerly proved,

places the same remark in a light still stronger ; and

shews plaiidy that, m this branch of knowledge.

Sect. 2. OP THE HUMAN MIND. 59

which is justly considered as the most certain of

any, the authority of the same hiws of belief which

are recognised in the ordinary pursuits of life, is

tacitly acknowledged. Deny the evidence of me-

mory as a ground of certain knowledge, and you

destroy the foundations of mathematical science, as

completely as if you were to deny the truth of the

axioms assumed by Euclid.

The foregoing examples sufficiently illustrate the

nature of that class of truths which I have called

Fundamental Laxvs ofHuman Belief, or Primary

Elements ofHuman Reason. A variety of others,

not less important, might be added to the list ;*

but these I shall not at present stop to enumerate, as

my chief object, in introducing the subject here,

was to explain the common relation in which they

all stand to deductive evidence. In this point of

view, two analogies, or rather coincidences, between

the truths which we have been last considering, and

the mathematical axioms which were treated of

formerly, immediately present themselves to our

notice.

1. From neither of these classes of truths can any

direct inference be drawn for the farther enlarore-

ment of our knowledge. This remark has been

already shewn to hold universally with respect, to

the axioms of geometry ; and it applies equally to

what I have called Fundamental Laws of HumanBelief. From such propositions as these,—/ ejcist

;

* Such, for example, as our belief of the existence of efficient

causes; our belief of the existence of other intelligent beings

besides onrselves, &c. «Scc.


Iam the same person to-day that I was yesterday ;

the material world has an existence independent ofmy mind ; the general laxvs ofnature will contifiue^

in future^ to operate uniformly as in time past,—no inference can be deduced, any more than from

the intuitive truths prefixed to the Elements of

Euclid. Abstracted from otlier data, they are per-

fectly barren in themselves ; nor can any possible

combination of them help the mind forward one

single step in its progress. It is for this reason,

that, instead of calling them, witli some other writers,

f,rSt principleSy I have distinguished them by the

i\i\eo^fundamental laws of belief; the former word

seeming to me to denote, according to common

usage, some fact, or some supposition, from which

a series of consequences may be deduced.

If the account now given of these laws o/' belie/'

be just, the great argument which has been com-

monly urged in support of their authority, and

which manifestly confounds them with what are pro-

perly called principles cfreasoning,* is not at all

* Aristotle himself has more than once made this remark

;

more particularly in discussing the absurd question, Whether it

be possible for the same thing to be and not to be ? h'îuti S'i khi

•mto (fro<fuxvvvî vivtt Si' cfrttiituinair, trri yseg uâthurtu, to /um yiveer-

aj'uvetrtv ttiroftiît iiv*t. m *Te<gor y*^ at .SsZ/ôr 'sitts /ahJ' ourvc «/»*«

»rroSu^n Aristut. Metaphys. Vol. II. p. 873. Edit. Du Val.

" But there are some who, throutrh ignorance, make an at-

*' tempt to prove even this principle (that it is impossible for the

" same thing to be and not to be.) lor it is a mark of ignorance,

•' not to be able to distinguish those things which ought to be de-

" monstrated from things of which no demonstration should be

" attempted. In truth, it is altogether impossible that every-

Sect. 2. OF THE HUMAN MIND. 6i

applicable to the subject ; or at least does not rest

the point in dispute upon its right foundation. If

there were no first principles (it has been said), or,

in other words, if a reason could be given for every-

thing, no process of deduction could possibly be

brought to a conclusion. The remark is indisput-

ably true ; but it only proves (what no logician of

the present times will venture to deny) that the

mathematician could not demonstrate a single theo-

rem, unless he were first allowed to lay down his

definitions ; nor the natural philosopher explain or

account for a single phenomenon, unless he were

allowed to assume, as acknowledged facts, certain

general laws of nature. What inference does this

afford in favour of that particular class of truths to

which the preceding observations relate, and against

which the ingenuity of modern sceptics has been

more particularly directed ? If I be not deceived,

these truths are still more intimately connected with

the operations of the reasoning faculty than has been

generally imagined ; not as the principles (appât)

from which our reasonings set out, and on which

they ultimately depend ; but as the necessary con-

*' thing should be susceptible of demonstratioti ; otherwise the

" process would extend to infinity, and, alter all our labour, no-

" thing would be gained." In the sentence immediately pre-

ceding this quotation, Aristotle calls the maxim in question,

fitfiMtrctm tmt ct^x"' Trua-m, " the most certain of all principles.''

To the same purpose, Dr Reid has said :" I hold it to be ccr-

" tain, and even demonstrable, that all knowledge got by reason-

'* ing must be built on first principles. This," he adds, *' is as

" certain as that every house must have a foundation."—£wtf//.>

on Int. Pouers, p. 558, 4to edit.

6*2 ELEMENTS OF THE PHILOSOPHY Chap. L

ditions on which every step of the deduction tacitly

proceeds ; or rather (if I may use the expression) as

essential elements which enter into the composition

of reason itself.

•2. In this last remark I have anticipated, in some

measure, what I had to state with respect to the

second coincidence alluded to, between mathematical

axioms, and the other propositions which I have

comprehended under the general title o?fundamen-

tal laws ofhuman belief As the truth of axioms

is virtually presupposed or implied in the successive

steps of every demonstration, so, in every step of our

reasonings concerning the order of Nature, we pro-

ceed on the supposition, that the laws by which it is

regulated will continue uniform as in time past

;

and that the material universe has an existence in-

dependent of our perceptions. I need scarcely add,

that, in all our reasonings whatever, whether they

relate to necessary or to contingent truths, our own

personal identity, and the evidence of memory, are

virtually taken for granted. These different truths

all agree in this, that they are essentially involved

in the exercise of our rational powers ; although, in

themselves, they furnish no principles or data by

which the sphere of our knowledge can, by any in-

genuity, be enlarged. They agree farther in being

tacitly acknowledged by all men, learned or ignorant,

without any formal enunciation in words, or even any

conscious exercise of reflection. It is only at that

period of our intellectual progress when scientific

arrangements and metaphysical refinements begin

to be introduced, that they become objects of at-

Sect. 2. OF THK HUMAN MIND. C)3

tention to the mind, and assume the form of pro-

positions.

In consequence of these two analogies or coinci-

dences, I should have been inclined to comprehend,

under the general title of adioms, all the truths

which have been hitherto under our review, if the

common usage of our language had not, in a great

measure, appropriated that appellation to the axioms

of mathematics ; and if the view of the subject

which I have taken, did not render it necessary for

me tD direct the attention of my readers to the wide

diversity between the branches of knowledge to

which they are respectively subservient.

I was anxious also to prevent these truths from

being all identified, in point of logical importance,

under the same name. The fact is, that the one

class (in consequence of the relation in which they

stand to the demonstrative conclusions of geometry),

are comparatively of so little moment, that the for-

mal enumeration of them was a matter of choice

rather than of necessity; whereas the other class

have unfortunately been raised, by the sceptical con-

troversies of modern times, to a conspicuous rank in

the philosophy of the humau mind. I have thought

it more advisable, therefore, to hestow on the latter

an appropriate title of their own ; without, however,

going so far as to reject altogether the phiaseology

of those who have annexed to the word (Lviom a

more enlarged meaning than that which I have

usually given to it. Little inconvenience, indeed, can

arise from this latitude in the use of the term ; pro-

vided only it be always confined to those ultimate

6^ ELEMENTS OP THE PHILOSOPHY Chap. I.

laws of belief, which, although they form the first

elements of human reason, cannot with propriety be

ranked among the principles from which any of our

scientific conclusions are deduced.

Corresponding to the extension which some late

writers have given to axioynSy is that of the province

which they have assigned to intuition; a term

which has been applied, by Dr Beattie and others,

not only to the power by which we perceive the

truth of the axioms of geometry, but to that by

which we recognise the authority of the fundamen-

tal laws of belief, when we hear them enunciated in

language. My oidy objection to this use of the

word is, that it is a departure from common practice ;

according to which, if I be not mistaken, the proper

objects of intuition are propositions analogous to the

axioms prefixed to Euclid's Elements. In some

other respects, this innovation might perhaps be re-

garded as an improvement on the very limited and

imperfect vocabulary of which we are able to avail

ourselves in our present discussions.*

* According to Locke, \vc have the knowledge of our own

existence by intuition ; of the existence of God by demonstration ;

and of other things by sensation. Book iv. chap. ix. § 2.

This use of the word intuition seems to be somewhat arbitrary.

The reality of our own existence is a truth which bears as little

analogy to the axiom« of mathematics, as any other primary

truth whatever. If the province of intuition, therefore, be extend-

ed as far as it has been carried by Locke in the foregoing

sentence, it will not be easy to give a good reason why it should

not be enlarged a little farther. The words intuition and de-

monstration, it must not be forgotten, have both of them an

etymological reference to the sense of seeing ; and when \st

Sect. 2. OF THE HUMAN MIND* G5

To the class of trutlis which I have here called

laxcs of belief, or elements of reasoii, the title of

principles of common sense was long ago given by

Father Butfier, whose language and doctrine con-

cerning them bears a very striking resemblance to

those of some of our later Scotish logicians. This,

at least, strikes nie as the meaning which these writ-

ers 171 general annex to the phrase ; although all of

them have frequently employed it with a far greater

degree of latitude. When thus limited in its accep-

tation, it is obviously liable, in point of scientific ac-

curacy, to two very strong objections, both of which

have been already sufficiently illustrated. The first

is, that it applies the appellation of principles to

laws of belief from which no inference can be dedu-

ced ; the second, that it refers the origin of these

laws to common sense. *—Nor is this phraseology

more agreeable to popular use than to logical preci-

sion. If we were to suppose an individual, whose

conduct betrayed a disbelief of his own existence, or

of his own identity, or of the reality of surrounding

objects, it would by no means amount to an adequate

description of his condition to say, that he was des-

titute of common sense. We should at once pro-

wish to express, in the strongest terms, the most compkte evi.

dence which can be set before the mind, we compare it to the

light of noon-day ;—in other words, we compare it to what IMr

Locke here attempts to degrade, by calling it the evidence of

sensation.

* See the preceding part of this section, with respect to the

Word principle ; and the Account of Reid's Life, for some re-

marks on the proper meaning of the phrase eommon sense,

VOL. II. E


' nounce him to be destitute of reason, and would no

longer consider him as a fit subject of discipline or

of punishment. The former expression, indeed,

would only imply that he was apt to fall into absurdi-

ties and improprieties in the common concerns of

life. To denominate, therefore, such laws of belief

as we have now been considering, constituent ele-

ments of human reason, while it seems quite unex-

ceptionable in point of technical distinctness, cannot

be justly censured as the slightest deviation from

our habitual fonns of speech. On the same grounds,

it may be fairly questioned, whether the word rea-

son would not, on some occasions, be the best sub-

stitute v/liich our language affords for intuition, in

that enlarged acceptation which has been given to it

of late. If not quite so definite and precise as might

be wished, it would be at least employed in one of

those significations in which it is already familiar to

every ear ; whereas the m.eaning of intuition, when

used for the same purpose, is stretched veiy far be-

yond its ordinaiy limits. And in cases of this sort,

where we have to choose between two terms, neither

of which is altogether unexceptionable, it will be

found much safer to trust to the context for restrict-

ing, in the reader's mind, what is too general, than

for enlarging what use has accustomed us to inter-

pret in a sense too narrow.

I must add, too, in opposition to the high authori-

ties of Dr Johnson and Dr Beattie, * that, for many

* Dr Johnson's definition of Reason was before quoted. The

following is that given by Dr Beattie :

" Reason is used by those who are most accurate in distin*


years past, reason has been very seldom used by phi-

losophical writers, or, indeed, by correct writers of

any description, as synonymous with the power of

reasoning. To appeal to the light ofhuman reason

frwn the reasonings of the schools, is surely an ex-

pression to which no good objection can be made, on

the score either of vagueness or of novelty. Nor

has the etymological affinity between these two

words the slightest tendency to throw any obscuri-

ty on the foregoing expression. On the contrary,

this affinity may be of use in some of our future argu-

ments, by keeping constantly in view the close and in-

separable connection which will be afterwards shewn

to exist between the two diflPerent intellectual opera-

tions which are thus brought into immediate contrast.

The remarks which I have stated in the two pre-

ceding sections, comprehend everything of essen-

tial importance which I have to offer on this article

of logic. But the space which it has occupied for

nearly half a century, in some of the most noted phi-

losophical works which have appeared in Scotland,

lays me under the necessity, before entering on a

new topic, of introducing, in this place, a few cri-

tical strictures on the doctrines of my predecessors.

" guishing, to signify that power of the Human Mind by which

" we draw inferences, or by which we are convinced, that a re-

" lation belongs to two ideas, on account of our having found

" that these ideas bear certain relations to other ideas. In a

" word, it is that faculty which enables us, from relations or ideas

" that are known, to investigate such as are unknown, and with-

" out which we never could proceed in the discovery of truth a

" single step beyond first principles or intuitive axioms."

—

Essay

on Truth, Part I. chap. i.

08 ELEMENTS OF THE PHILOSOniY Chap. I.

Section III.

Cojitinuaimi of the Subject.—Critical Remarks on

some late Controversies to which it has given rise,

—Of the Appeals_idiich Dr Reid and some other

Modern JVriters have made^ in their Philosophi-

cal DiscussionSy to Common Seiise, as a Criterion

of Truth.

I OBSERVED, in a former part of this work, that

Dr Reid acknowledges the Berkeleian system to be a

logical consequence of the opinions universally ad-

mitted by the learned at the time when Berkeley

wrote. In the earlier part of his own life, accord-

ingly, he informs us, that he was actually a convert

to the scheme of immaterialism ; a scheme which he

probably considered as of a perfectly inoffensive ten-

dency, as long as he conceived the existence of the

material world to be the only point in dispute.

Finding, however, from Mr Hume's writings, that,

along with this paradox, the ideal theory necessari-

ly involved various other consequences of a very dif-

ferent nature, he was led to a careful examination of

the data on which it rested ; when he had the satis-

faction to discover that its only foundation was a hy-

pothesis, unsupported by any evidence whatever but

the authority of the schools. *

* It was not, therefore (as has very generally been imagined

by the followers of Berkeley), from any apprehension of danger

in his argument against the existence of matter, that Reid was

induced to call in question the ideal theory ; but because he

thought that ]\Ir Hume had clearly shewn, by turning Berkeley's

weapons against himself, that this theory was equally subversive

Sect. 3. OF THE HUMAN MIND. (39

From this important concession of a most impar-

tial and competent judge, it may be assumed as a fact,

that, till the refutation of the ideal theory in his

own *' Inquiry into the Human Mind," the parti-

sans of Berkeley's system remained complete masters

of the controversial field ; and yet, during the long

period which intei*vened, it is well known how little

impression that system made on the belief of our

soundest philosophers. Many answers to it were at-

tempted, in the meantime, by various authors, both

in this country and on the Continent ; and by one

or other of these, the generality of the learned pro-

fessed themselves to be convinced of its futility ;

—

the evidence of the conclusion (as in many other

cases) supporting the premises, and not the premises

the conclusion. * A very curious anecdote, in il-

of the existence of 7ni/}d. The ultimate object of Berkeley and

of Reid was precisely the same ; the one asserting the existence

of matter from the very same motive which led the other to

deny it.

When I speak of Reid's asserting the existence of matter, I do

not allude to any new pioofs which he has produced of the fact.

This he rests on the evidence of sense, as he rests the existence

of the mind on the evidence of consciousness. All that he pro-

fesses to have done is, to shew the inconclusivcness of Berkeley's

argument against the former, and that of Hume against the lat-

ter, by refuting the ideal hypothesis which is the common foun-

dation of both.

* The impotent, though ingenious attempt of Berkeley (not

many years after the date of his metaphysical publications), to

shake the foundations of the newly invented method of Fluxions,

created, in the public mind, a strong prejudice against him, as a

sophistical and paradoxical disputant ; and operated as a more

powerful antidote to the scheme of immaterialism, than all the

reasonings which his contemporaries were able to oppose to it.

70 ELEiMENTS OF THE PHILOSOPHY Chap. I.

lustration of this, is mentioned in the life of DrBerkeley. After the publication of his book, it ap-

pears that he had an interview with Dr Clarke ; in

the course of which, Clarke (it is said) discovered a

manifest unwillingness to enter into the discussion,

and was accused by Berkeley of a want of candour. *

—The story (which, if I recollect right, rests on the

authority of Whiston) has every appearance of au-

thenticity ; for as Clarke, in common with his anta-

gonist, regarded the principles of the ideal theory

as incontrovertible, it was perfectly impossible for

him, with all his acuteness, to detect the flaw to

which Berkeley's paradox owed its plausibility. In

such circumstances, would it have been unphiloso-

phical in Clarke to have defended himself, by say-

ing : " Your conclusion not only contradicts those

" perceptions of my senses, the evidence of which I

*' feel to be irresistible ; but, by annihilating space

*' itself as an external existence, bids defiance to a

" conviction inseparable from the human under-

" standing j and, therefore, although I cannot point

This unfavourable impression was afterwards not a little confirm-

ed, by the ridicule which he incurred in consequence of his

pamphlet on the Virtues of Tar-water ; a performance, however,

of which it is but justice to add, that it contains a great dt?al

more, both of sound philosophy and of choice learning, than could

have been expected from the subject.

* Philosophical Essays, Note F.

That Clarke would look upon the Berkeleian theory with more

than common feelings of suspicion and alarm, may be easily con-

ceived, when it is recollected that, by denying the independent

existence both of space and of time, it put an end at once to his

celebrated argument a priori, for the existence of God.


" out the precise oversight which has led you astray,

" there must necessarily be some error, either in

*' your original datOy or in your subsequent reason-

*• ing." Or, supposhig Clarke to have perceived,

as clearly as Reid, that Berkeley's 7'easoning was

perfectly unexceptionable, might he not have ad-

ded,—" The conclusion which it involves is a de-

" monstration in the form of a rediictio ad absur-

" diwi, of the unsoundness of the ideal theory, on** which the whole of your argument is built.'* *

I am far from supposing that Berkeley would have

* I acknowledge, very readily, that the force of this indirect

mode of reasoning is essentially different, in mathematics, from

what it is in the other branches of knowledge ; for the object of

mathematics (as will afterwards more fully appear), not being

truth, but systematical connection and consistency, whenever two

contradictory propositions occur, embracing evidently the only

possible suppositions on the point in question, if the one can be

shewn to be incompatible with the definitions or hypotheses on

which the science is founded, this may be regarded as perfectly

equivalent to a direct proof df the legitimacy of the opposite con-

clusion. In other sciences, the force of a reductio ad absurdum

depends entirely on the maxim, " That truth is always consistent

" with itself;" a maxim which, however certain, rests evidently

on grounds of a more abstract and metaphysical nature than the

indirect demonstrations of geometry. It is a maxim, at the same

time, to which the most sceptical writers have not been able to

refuse their testimony. " Truth," says Mr Hume himself, " is

'* one thing, but errors are numberless, and every man has a dif-

" ferentone."

The unity, or systematical consistency of truth, is a subject

which well deserves to be farther prosecuted. It involves many

important consequences, of which Mr Hume does not, from the

general spirit of his philosophy, seem to have been sufficiently

aware.

7^ ELEMENTS OF THE PHILOSOPHY Chap. I.

admitted this consideration as decisive of the point

in dispute. On the contrary, it appears from his

writings, that the scheme of immaterialism was, in

his opinion, more agreeable to popular belief, than

the received theories of philosophers concerning

the independent existence of the external world

;

nay, that he considered it as one of the many ad-

vantages likely to result from the universal adoption

of his system, that " men would thereby be reduced

" from paradoxes to common sense.^^

The question, however, if not decided by this dis-

cussion, would at least have been brought to a short

and simple issue ; for the paramount authority of

the common sense or common reason of mankind,

being equally recognised by both parties, all that re-

mained for their examination was,—whether the

belief of the existence, or that of the non-existence

of matter, was sanctioned by this supreme tribunal ?

For ascertaining this point, nothing more was ne-

cessary than an accurate analysis of the meaning an-

nexed to the word emstence ; which analysis would

have at once shewn, not only that we are irresistibly

led to ascribe to the material world all the indepen-

dent reality which this word expresses, but that it is

from the material world that our first and most satis-

factory notions of existence are drawn. The mathe-

matical affections of matter (extension and figure)

to which the constitution of the mind imperiously

farces us to ascribe an existence, not only indepen-

dent of our perceptions, but necessary and eternal,

might more particularly have been pressed upon

Berkeley, as proofs how incompatible his notions

St^ct. 3. OF THE HUMAN MIND. 73

were with those laws of belief, to which the learned

and the unlearned must in common submit.*

But farther (hi order to prevent any cavil about

the foregoing illustration), we shall suppose that

Clarke had anticipated Hume in perceiving that the

ideal theory went to the annihilation of mind as well

as of matter; and that he had succeeded in proving,

to the satisfaction of Berkeley, that nothing existed

in the universe but impressions and ideas. Is it

possible to imagine that Berkeley would not im-

mediately have seen and acknowledged, that a theory

which led to a conclusion directly contradicted by

the evidence of consciousness, ought not, out of

respect to ancient authority, to be rashly admitted j

and that, in the present instance, it was much more

philosophical to argue from the conclusion against

the hypothesis, than to argue from the hypothesis

in proof of the conclusion ? No middle course, it

is evident, was left him between such an acknow-

ledgment, and an unqualified acquiescence in those

very doctrines which it was the great aim of his

system to tear up by the roots.

The two chief objections which I have heard

urged against this mode of defence, are not perfectly

consistent with each other. The one represents it

as a presumptuous and dangerous innovation in the

established rules of philosophical controversy, calcu-

lated to stifle entirely a spirit of liberal inquiry

;

while the other charges its authors with all the

meanness and guilt of literary plagiarism. I shall

Sec Note (B.)


offer a few slight remarks on each of these accusa-

tions.

1. That the doctrine in question is not a new

one, nor even the language in which it has been

recently stated an innovation in the received phra-

seology of logical science, has been shewn by DrReid, in a collection of very interesting quotations,

which may be found in different parts of his Essays

on the Intellectual Powers of Man, more particularly

in the second chapter of the sixth essay. Nor has

this doctrine been generally rejected even by those

writers who, in their theories, have departed the far-

thest from the ordinary opinions of the world. Berke-

ley has sanctioned it in the most explicit manner, in a

passage already quoted from his works, in which

he not only attempts the extraordinary task of re-

conciling the scheme of immaterialism with the

common sense of mankind, but alleges the very cir-

cumstance of its conformity to the unsophisticated

judgment of the human race, as a strong argument

in its favour, when contrasted with the paradoxical

doctrine of the independent existence of matter.

The ablest advocates, too, for the necessity of human

actions, have held a similar language ; exerting their

ingenuity to shew, that there is nothing in this tenet

which does not perfectly accord with our internal

consciousness, when our suppossed feelings of liberty,

with all their concomitant circumstances, are accu-

rately analyzed, and duly weighed.* In this respect,

* This, I own, appears to me the only argument for the scheme

of necessity, which deserves a moment's consideration, in the

Sect, 3. OF THE HUMAN MIND. 7^

Mr Hume forms almost a solitary exception, avow-

ing, with the greatest frankness, the complete re-

pugnance between his philosophy and the laws of

belief to which all men are subjected by the consti-

tution of their nature. ** I dine ; I play a game*' at backgammon ; I converse, and am happy with

*' my friends ; and when, after three or four hours

'* of amusement, I would return to these specula-

*' tions, they appear so cold, so strained, and so

" ridiculous, that I cannot find in my heart to enter

" into them any further. Here, then, I find my-" self absolutely and necessarily determined to live,

" and talk, and act, like other people, in tlie com-

" mon affairs of life.*'*

Even Mr Hume himself, however, seems at times

to forget his sceptical theories, and sanctions, by

his own authority, not only the same logical maxims,

but the same mode of expressing them, which has

been so severely censured in some of his opponents.

*' Those," he observes, "who have refused the reality

" of moral distinctions, may be ranked among the

" disingenuous disputants. The only way of convert-

present state of the controversy : and it is certainly possible to

state it in such a form as to give it some degree of plausibility to

a superficial inquirer. On this point, however, as on many

others, our Jirst and third thoughts will be found perfectly to

coincide ; a more careful and profound examination of the ques-

tion infallibly bringing back to their natural impressions, those

who reflect on the subject with candour and with due attention.

Having alluded to so very important a controversy, I could not

help throwing out this hint here. The farther prosecution of it

would be altogether foreign to my present purpose,

* Treatise of Human Nature, Vol. I. p. 467,

76 ELEBIENTS OF THE PHILOSOPHY Cliap. I.

*' ing an antagonist of this kind is, to leave him** to himself; for, finding that nobody keeps up" the controversy with him, 'tis probable he will at

" last, of himself, from mere weariness, come over

*' to the side of common sense and reason." *

To the authorities which have been already pro-

duced by Reid and his successors, in vindication of

that mode of arguing which is now under our re-

view, I shall beg leave to add another, which, as far

as I know, has not yet been remarked by any of

them ; and which, while it effectually removes from

it the imputation of novelty, states, in clear and

forcible terms, the grounds of that respect to which

it is entitled, even in those cases where it is opposed

by logical subtleties which seem to baffle all our

powers of reasoning.

" What is it," said some of the ancient sophists,

*' which constitutes what we call little, much, long,

*' broad, small, or great ? Do three grains of corn

" make a heap ? The answer must be—No. Do*' four grains make a heap ? You must make the

" same answer as before.—They continued their in-

" terrogations from one grain to another, without

*' end ; and if you should happen at last to answer,

" herê is a heap^ they pretended your answer was

" absurd, inasmuch as it supposed, that one single

*' grain makes the difference between what is a

*' heap, and what is not. I might prove, by the

" same method, that a great drinker is never drunk.

** Will one drop of wine fuddle him ?—No. Two" drops, then ? By no means ; neither three nor

* Inq<iiry concerning the Principles of Moriils.

Sect. 3. OV THE HUMAN MIND. 77

"four. I might thus continue my interrogations

* from one drop to another ; and if, at the end of

" the 999th drop, you answered lie is not fuddled,

" and at the 1000th he is, I should be entitled to

" infer, that one single drop of wine makes the dif-

" ference between being drunk and being sober

;

" which is absurd. If the interrogations went on

*' from bottle to bottle, you could easily mark the

" difference in question. But he who attacks you

" with a soriteSy is at liberty to choose his own" weapons ; and, by making use of the smallest

" conceivable increments, renders it impossible for

" you to name a precise point which fixes a sen-

" sible limit between being drunk and being sober ;

" between what is little and what is great ; between

" what is enough and what is too much. A man" of the world would laugh at these sophistical

" quibbles, and would ajjpeal to common sense ;

" to that degree of knowledge which, in common*' life, is sufficient to enable us to establish such dis-

" tinctions. But to this tribunal a professed dialec-

" tician was not permitted to resort ; he was obliged

*' to answer in form ; and if unable to find a solu-

** tion according to the rules of art, his defeat was*' unavoidable. Even at this day, an Irish Tutor, *

* It is remarkable of this ingenious, eloquent, and gallant na-

tion, that it has been for ages distinguished, in the universities on

the Continent, for its proficiency in the school logic. Le Sage

(who seems to have had a very just idea of the value of this ac-

complishment) alludes to this feature in the Irish character, in

the account given by Gil Bias of his studies at Oviedo. " Je" m'appliquai aussi k la logique, qui m'apprit d, raisonner beau-

" coup. J'aimois tant la dispute, que j'arretois les passans, con-


" who should harass a Professor of Salamanca with

** similar subtleties, and should receive no other an-

** swer but this,

—

common sense^ and the general

" consent of mankind, sujjicie7itltj shew that your" inferences arefalse,—would gain the victory ; his

*' antagonist having declined to defend himself with

** those logical weapons with which the assault had*' been made."

Had the foregoing passage been read to the late

Dr Priestley, while he was employed in combating

the \vritings of Reid, Oswald, and Beattie, he would,

I apprehend, without hesitation, have supposed it to

be the production of one of their disciples. Thefact is, it is a translation from Mr Bayle, an author

who was never accused of an undue deference for

established opinions, and who was himself undoubt-

edly one of the most subtile disputants of modern

times. *

From this quotation it clearly appears, not only

that the substance of the doctrine maintained by

these philosophers is of a much earlier date than

their writings ; but that, in adopting the phrase

" nus ou inconnus, pour leur proposer des argumens. Je

** m'addressois quelquefois a. des figures Hibernoises, qui ne

" demandoient pas mieux, ct il falloil alors nous voir disputer.

•' Quels gestes, quelles grimaces, quelles contorsions ! nos 3?eux

" etoient pleins de fureur, et nos bouches ecumantes. On nous

" devoit plulot prendre pour des posscd6s que pour des philo-

" sophes.*'

* See Bayle's Dictionary, article Chrysippe. I have availed

myself, in the above translation (with a few retrenchments and

corrections), of that which is given in the English Biographical

and Critical Dictionary.


common sense, to express that standard or criterion

of truth to which they appealed, they did not de-

part from the language previously in use among

the least dogmatical of their predecessors.

In the passage just quoted from Bayle, that

passion for disputation which, in modern Europe,

has so often subjected the plainest truths to the

tribunal of metaphysical discussion, is, with great

justness, traced to the unlimited influence which

the school logic maintained for so many ages over

the understandings of the learned. And although,

since the period when Bayle wrote, this influence

has everywhere most remarkably declined, it has yet

left traces behind it in the habits of thinking and

judging prevalent among speculative men, which

are but too discernible in all the branches of science

connected with the philosophy of the Mind. In

illustration of this remark, it would be easy to pro-

duce a copious list of examples from the literary

history of the eighteenth centuiy ; but the farther

prosecution of the subject here would lead me aside

from the conclusions which I have at present in

view. I shall therefore content myself with op-

posing, to the contentious and sceptical spirit be-

queathed by the schoolmen to their successors, the

following wise and cautious maxims of their master,

—maxims which, while they illustrate his anxiety

to guard the principles of the demonstrative sciences

against the captiousness of sophists, evince the re-

spect which he conceived to be due by the philoso-

pher to the universal reason of the human race.

** Those things are to be regarded nsjirst truths^

80 ELEMENTS OF THE PHILOSOPHY Ciiap. I.

*' the credit of which is not derived from other

*' truths, but is inherent in themselves. As for

** probable truths, they are such as are admitted by** all men, or by the generalitij of men, or by "wise

*' men ; and, among these last, either by all the

" wise, or by the generality of the wise, or by such

" of the wise as are of the highest authority.'* *

The argument from Universal Consent, on which

so much stress is laid by many of the ancients, is

the same doctrine with the foregoing, under a form

somewhat different. It is stated with great simpli-

city and force by a Platonic philosopher, in the fol-

lowing sentences

:

" In such a contest, and tumult, and disagree-

" ment (about other matters of opinion), you may" see this one law and language acknowledged by

" common accord. This the Greek says, and

" this the barbarian says ; and the inhabitant of the

** continent, and the islander ; and the wise, and

" the unwise.'* t

It cannot be denied, that against this summary

* E9"TI it aX«S« fAiV xctt TTÛTity Tet /MX ii iTi^csi, ttW* itiulur f;^9»T«

<r»» TrirTit, EkTsI* it, tei JoKouyrai vetviv, » tojc vhuvntf, n reic ffo^tw

KCit TOOTO/C, « TO/f frcLTIV, X To/c TrMtTTOtCt TO/C fJt!X.\tfTlt, -yVUÎfjlOlt, Kttt

tySoôic Aristot. Top. Lib. I. cap. i. (Vol. I. p. 180, ed. Du Val.)

t E» ttvuTU ii irtXi/jta kI Tct<Tii t^ intqiuitit eva /cTcjc a.1 iv a-ao-j) y» cfjti-

»»»4y rofxov t^ fôyo*, &c. Tuvrtiii i 'Ekkhv >^ty(i, t^ e Botj/S^tgec Mytt, i^

i if/ru^vTm, t^ e*x«TT/o{, >ô »-«f9f, t^ o' Aeroftu—Max. Tyr. (speak-

ing of the existence of the Deity,) Dis. I.

" Una in re consensio omnium gentium lex nature putanda

" est."—C/c. l.Tusc.

" Multum dare solemus praesumptioni omnium hominum

:

" Apud nos veritatis argumentum est, aliquid omnibus videri.'-

&c. &c.

—

Sen, Ep. 11 7-

Sect. 3. OF THE HITMAN MIND. 81

species of logic, when employed without any colla-

teral lights, as an infallible touchstone of philoso-

phical truth, a strong objection immediately occurs.

By what test (it may be asked) is a principle of

common sense to be distinguished from one of those

prejudices to which the whole human race are irresist-

ibly led, in the first instance, by the very consti-

tution of their nature ? If no test or criterion of

truth can be pointed out but universal consent, may

not all those errors which Bacon has called idola

tribiis claim a right to admission among the incon-

trovertible axioms of science ? And might not the

popular cavils against the supposition of the earth's

motion, which so long obstructed the progress of

the Copernican system, have been legitimately op-

posed, as a reply of paramount authority, to all the

scientific reasonings by which it was supported ?

It is much to be wished that this objection, of

which Dr Reid could not fail to be fully aware, had

been more particularly examined and discussed in

some of his publications, than he seems to have

thought necessary. From different parts of his

works, however, various important hints towards a

satisfactoi-y answer to it might be easily collected. *

At present, I shall only remark, that, although uni'

versality of beliefh one of the tests by which (accord-

ing to him) a principle of common sense is charac-

terized, it is not the only test which he represents

as essential. Long before his time, Father Buffier,

* See, in particular, Essays on the Int, Powers, p. 565, d seq.

4to edit.

VOL. 11. F

8^ ELEMENTS OF THE PHILOSOPHY Chap. I.

in his excellent treatise on First Truths, had laid

great stress on two other circunlstances, as criteria

to be attended to on such occasions ; and although

I do not recollect any passage in Reid where they

are so explicitly stated, yet the general spirit of his

reasonings plainly shews, that he had them constant-

ly in view in all the practical applications of his

doctrine. The J?r5^ criterion mentioned by Buffier

is, *' That the truths assumed as maxims of com-" mon sense should be such, that it is impossible for

" any disputant either to defend or to attack them,

" but by means of propositions which are neither

" more manifest nor more certain than the proposi-

** tions in question.'* The second criterion is,

*' That their practical influence should extend even

" to those individuals who affect to dispute their au-

" thority."

To these remarks of Buffier, it may not be alto-

gether superfluous to add, that, wherever a preju-

dice is found to obtain universally among mankind

in any stage of society, this prejudice must have

some foundation in the general principles of our na-

ture, and must proceed upon some truth or fact in-

accurately apprehended, or erroneously applied.

The suspense of judgment, therefore, which is pro-

per with respect to particular opinions, till they be

once fairly examined, can never justify scepticism

with respect to the general laws of the human mind.

Our belief of the sun's motion is not a conclusion to

which we are necessarily led by any such law, but an

inference rashly drawn from the perceptions of sense,

which do not warrant such an inference. All that

12


we see is, that a relative change of position between

us and the sun takes place ; and this fact, which is

made known to us by our senses, no subsequent dis-

covery of philosophy pretends to disprove. It is

not, therefore, the evidence of perception which is

overturned by the Copernican system, but a judg-

ment or inference of the understanding, of the rash-

ness of which every person must be fully sensible,

the moment he is made to reflect with due atten-

. tion on the circumstances of the case ; and the doc-

trine which this system substitutes instead of our first

crude apprehensions on the subject, is founded, not

on any process of reasoning a priori., but on the de-

monstrable inconsistency of these apprehensions with

the various phenomena which our pei'ceptions pre-

sent to us. Had Copernicus not only asserted the

stability of the Sun, but, with some of the Sophists

of old, denied that any such thing as motion exists in

the universe, his theory would have been precisely

analogous to that of the non-existence of matter ;

and no answer to it could have been thought of more

pertinent and philosophical, than that which Plato

is said to have given to the same paradox in the

mouth of Zeno, by rising up and' walking before his

eyes.

2. If the foregoing observations be just, they not

only illustrate the coincidence between Dr Reid's

general argument against those metaphysical para-

doxes which revolt connnon sense, and the maxims

of philosophical discussion previously sanctioned by

our soundest reasoners ; but they go far, at the same

time, to refute that charge of plagiarism in which he


has been involved, in common with two other Scot-

ish writers, who have made their stand in opposition

to Berkeley and Hume, nearly on the same ground.

This charge has been stated, in all its force, in the

preface to an English translation of Buffier's Premi-

eres Verites, printed at London in the year I78O ;

and it cannot be denied, that some of the proofs al-

leged in its support are not without plausibility. But

why suppose Reid to have borrowed from this learn-

ed Jesuit, a mode of arguing which has been fami-

liar to men in all ages of the world ; and to which,

long before the publication of Buffier*s excellent

book, the very same phraseology had been applied

by numberless other authors ? On this point, the

passage already quoted from Bayle is of itself decisive.

The truth is, it is a mode of arguing likely to occur

to every sincere and enlightened inquirer, when be-

wildered by sceptical sophistry ; and which, during

the long interval between the publication of the

Berkeleian theory, and that of Reid*s Inquiry, was

the only tenable post on which the conclusions of the

former could be combated. After the length to

which the logical consequences ofthe same principles

were subsequently pushed in the Treatise of Hu-man Nature, this must have appeared completely

manifest to all who were aware of the irresistible

force of the argument, as it is there stated ; and, in

fact, this very ground was taken as early as the year

1751, in a private correspondence with Mr Hume,

by an intimate friend of his own, for whose judg-

ment, both on philosophical and literaiy subjects, he

Sect. 3. OF THE HUMAW MIND. ^^

seems to have felt a peculiar deference.* I mention

this, as a proof that the doctrine in question was the

aiatural result of the state of science at tlie period

when Reid appeared ; and, consequently, that no

argument against his originality in adopting it, can

reasonably be founded on its coincidence with the

views of any preceding author.

A still more satisfactory reply to the charge of

plagiarism may be derived from this consideration,

that, in Buffier's Treatise, the doctrine which has

furnished the chief ground of accusation is stated

with far greater precision and distinctness than in

Dr Reid's^r^^ publication on the Human Mind;

and that, in his subsequent performances, after he

had perused the writings of Buffier, his phraseology

became considerably more guarded and consistent

•than before.

If this observation be admitted in the case of Dr

Reid, it will be found to apply with still greater

force to Dr Beattie, whose language, in various parts

of his book, is so loose and unsettled, as to afford de-

monstrative proof that it was not from Buffier he

derived the idea of his general argument. In con-

finnation of this, I shall only mention the first chap-

ter of the first part of his Essay, in which he at-

tempts to draw the line between common sense and

reason ; evidently confounding (as many other au-

thors of high reputation have done) the two very

different words reason and reasoinng. His account

of common sense, in the following passage, is liable

to censure in almost every line : " The term com-

* See Note (C.)


" man sense hath, in modern thiies, been used by

" philosophers, both French and British, to signify

*' that power of the mind which perceives truth, or

" commands belief, not by progressive argumenta-

" tion, but by an instantaneous, instinctive, and ir-

" resistible impulse ; derived neither from education

*' nor from habit, but from nature ; acting indepen-

*' dently on our will, whenever its object is present-

" ed, according to an established law, and therefore

^^ properli/ called sense,* and acting in a similar

* The doctrine of the schoolmen (revived in later times under

a form somewhat modified by Locke), which refers to sensation

the origin of all our ideas, has given rise to a very unwarrantable

extension of the word sense, in the writings of modern philoso-

phers. When it was first asserted, that " there is nothing in the

" intellect which does not come to it through the medium of

" sense," there cannot be a doubt that, by this last term, were

understood exclusively our powers of external perception. In

process of time, however, it came to be discovered, that there are

many ideas which cannot possibly be traced to this source ; and

which, of consequence, afford undeniable proof that the scholas-

tic account of the origin of our ideas is extremely imperfect.

Such was certainly the logical inference to which these discove-

ries should have led ; but, instead of adopting it, philosophers

have, from the first, shewn a disposition to save, as much as

possible, the credit of the maxims in which they had been edu-

cated, by giving to the word sense so great a latitude of mean-

ing, as to comprehend all the various sources of our simple ideas,

whatever these sources may be. " All the ideasy' says Dr

Hutcheson, " or the materials of our reasoning and judging, are

" received by some immediate powers of perception, internal or

" external, which we may call senses." Under the title of ittter-

nal senses, accordingly, many writers, particularly of the medical

profession, continue to this day to comprehend memory and ima-

gination, and other faculties, both intellectual and active.—(Vide


** manner upon all, or at least upon a great majority

** of mankind, and therefore properly called coM-

*' MON SENSE.*' *

" Reason," on the other hand (we are told by

the same author), " is used by those who are most

" accurate in distinguishing, to signify that power

" of the Human Mind by which we draw inferen-

'* ces, or by which we are convinced that a relation

" belongs to two ideas, on account of our having

" found that these ideas bear certain relations to

" other ideas. In a word, it is that faculty which

" enables us, from relations or ideas that are known" to investigate such as are unknown ; and without

" which we never could proceed in the discovery of

" truth a single step beyond first principles or intui-

" tive axioms." t " It is in this last sense,** he

adds, " that we are to use the word reason in the

" course of this inquiry.*'

These two passages are severely, and, I think,

justly animadverted on, in the preface to the English

translation of Buffier's book, where they are contrast-

Haller, Ehjnent. Physiologice, Lib. xvii.) Hence also the phrases

7noral sense, the senses of' beauts/ and harmony, and many of the

other peculiarities of Dr Hutcheson's language ; a mode of speak-

ing which was afterwards carried to a much more blameable ex-

cess by Lord Kaimes; Dr Beattie, in the passage quoted above,

has indirectly given his sanction to the same abuse of words

;

plainly supposing the phrase, common sense, not only to mean

something quite distinct from reason, but something which bears

so close an analogy to the powers of external sense, as' to be not

improperly called by the same name.

* Essay on Truth, p. 40, 2d edit.

+ Ibid. pp. 36, 37, 2d edit.


ed with the definition of common sense given by that

profound and original philosopher. From this de-

finition it appears, that, far from opposing commonsense and reason to each other, he considers them

either as the same faculty, or as faculties necessarily

and inseparably connected together. "It is a fa-

*' culty," he says, *' which appears in all men, or at

*' least in the far greater number of them, when" they have arrived at the age of reason, enabling

" them to form a common and uniform judgment,** on subjects essentially connected with the ordina-

" ry concerns of life."

That this contrast turns out greatly to the advan-

tage of Buffier * must, I think, be granted to his

* It is remarkable how little attention the writings of Buffier

have attracted in his own country, and how very inadequate to

his real eminence has been the rank commonly assigned to him

among French philosophers. This has perhaps been partly ow-

ing to an unfortunate combination which he thought proper to

make of a variety of miscellaneous treatises, of very unequal me-

rit, into a large work, to which ho gave the name of a Course of

the Sciences. Some of these treatises, however, are of great va-

lue;

particularly that on P?7-,s^ Truths, which contains (along

with some erroneous notions, easily to be accounted for by the

period when the author wrote, and the religious society with

which he was connected) many original and important views

concerning the foundations of human knowledge, and the first

principles of a rational logic, ^'oltairo, in his catalogue of the

illustrious writers who adorned the rei^>n of Louis XIV\ is one of

the very few French authors who have spoken of Buffier with

due respect. " Jl y a dans ses traites de metaphysique des mor-

" ceaux que Locke n'aurait pas desavoues, ct c'est le seul jesuite

" qui ait mis une philosophic raisonnable dans ses ouvrages."

Another French philosopher, too, of a very different school, and

certainly not disposed to overrate the talents of Bufifier, ha^, in a

Sect. 3. OF TÊ HUMAN MIND. 89

very acute and intelligent translator. But while I

make this concession in favour of liis" argument, I

must be allowed to add, that, in the same proportion

in which Dr Beattie falls short of the clearness and

logical accuracy of his predecessor, he ought to stand

acquitted, in the opinion of all men of candour, of

every suspicion of a dishonourable plagiarism from

his writings.

It is the doctrine itself, however, and not the com-

parative merits of its various abettors, that is likely

to interest the generality of philosophical students

;

and as I have always thought that this has suflPered

considerably in the public estimation, in consequence

of the statement of it given in the passage just

quoted from the Essay on Truth, I shall avail my-

self of the present opportunity to remark, how wide-

ly that statement differs from the language, not on-

ly of Buffier, but of the author's contemporary and

friend, Dr Reid, This circumstance I think it ne-

cessary to mention, as it seems to have been through

work published as lately as 1805, candidly acknowledged the

lights which he might have derived from the labours of his pre-

decessor, if he had been acquainted with them in an earlier stage

of his studies. Condillac, he also observes, might have profited

greatly by the same lights, if he had availed himself of their

guidance in his inquiries concerning the human understanding.

" Du moins est il certain, que pour ma part, je suis fort fache

" de ne connoitre que depuis tres peu de temps ces opinions du" Pore Bufficr; si je les avals vucs plutot enoncees quelque part,

" elles m'auraient epargne beaucoup de peines et d'hesitations.''

" Jeregrette beaucoup que Condillac, dans ses profondes ct

*' sagaces meditations sur I'intelligence humaine, n'ait pas fait

"plus d'attention aux idees du Pere Buffier," &c. &c.

—

Ele-

vens d'Ideologie,^)ar M. Destuii-Traci/, Tom. III. pp. 136, 137.

90 ELEMENTS OF THE PHILOSOPHY Chaj), 1.

the medium of Dr Beattie's Essay that most Eng-

lish writers have derived their imperfect informa-

tion conceraing Reid's philosophy.

" There is a certain degree of sense,** says this

last author, in his Essays on the Intellectual Powers

of Man, *' which is necessary to our being subjects

** of law and government, capable of managing our

" own affairs, and answerable for our conduct to

" others. This is called common sense, because it

" is common to all men with whom we can transact

" business."

" The same degree of undei'standing,** he after-

wards observes, " which makes a man capable of

*' acting with common prudence in life, makes him" capable of discerning what is true and what is false,

" in matters that are self-evident, and which he dis-

" tinctly apprehends.*' In a subsequent paragraph,

he gives his sanction to a passage from Dr Bentley,

in which common sense is expressly used as synony-

mous with natural light and reason, *

* Pages 522, 524, 4to edit. In the following verses of Prior,

the word reason is employed in an acceptation exactly coincident

with the idea which is, on most occasions, annexed by Dr Reid to

the phrase common sense :

" Note here, Lucretius dares to teach

" (As all our youth may learn from Creech,)" Tliat eyes weie made, but couhi not view,

'' Nor hands embrace, nor feet pursue,

*' But heedless Nature did produce

" The members first, and then the use;

" What each must act was yt>t unknown,

" Till all was moved by Chance alone.

" Blest for his sake be kuman reason,'' ^V^4ch came at last, the' late, in season."

—

Almu^ Canto I.


It is to be regretted, as a circumstance unfavour-

able to the reception of Dr Beattie*s valuable Essay

among accurate reasoners, that, in the outset of his

discussions, he did not confine himself to some such

general explanation of this phrase as is given in the

foresoino; extracts from Buffier and Reid, without

affecting a tone of logical precision in his definitions

and distinctions, which, so far from being necessary

to his intended argument, were evidently out of

place, in a work designed as a popular antidote

against the illusions of metaphysical scepticism.

The very idea, indeed, of appealing to common sense,

virtually implies that these words are to be under-

stood in their ordinary acceptation, unrestricted and

unmodified by any technical refinements and com-

ments. Tliis part of his Essay, accordingly, which

is by far the most vulnerable part of it, has been at-

tacked with advantage, not only by the translator

of Buffier, but by Sir James Steuart, in a very acute

letter published in the last edition of his works. *

While I thus endeavour, however, to distinguish

Dr Reid's definition of common sense from that of

Dr Beattie, I am far from considering even the lan-

guage of the former on this subject as in every in-

stance unexceptionable j nor do I think it has been

a fortunate circumstance (notwithstanding the very

high authorities which may be quoted in his vindi-

* To the honour of Dr Beattie it must be remarked, that his

reply to this letter (which may be found in Sir James Steuart's

works) is written in a strain of forbearance and of good humour,

which few authors would have been able to maintain, after being

handled so roughly.

1)2 ELEMENTS OF THE PHILOSOPHY Chap. I.

cation), that he attempted to incoi-porate so vague

and ambiguous a phrase with tlie appropriate terms

of logic. My chief reasons for this opinion I have

stated, at some ler.gtli, ni an account published a few

years ago of Dr Reid's Life and Writings. *

One very unlucky consequence has unquestionably

resulted from the coincidence of so many writers

connected with this northern part of the island, in

adopting, about the same period, the same phrase, as

a sort of philosophical w-atch-word ;—that, although

their views differ widely in various respects, they

* In consequence of the ambiguous meaning of this phrase,

Dr Reid sometimes falls into a sort of play on words, which I

have often regretted. " If this be philosophy," says he, on one

occasion, " I renounce her guidance. Let my soul dwell with

" common senseJ^ {Inquiry into the Human Jtfzwrf, Chap. I.

Sect. 3. See also Sect. 4, of the same chapter.) And in ano-

ther passage, after quoting tlie noted saying of Hobbes, that

" when reason is against a man, a man will be against reason;"

he adds, *' This is equally applicable to common sense.'*^ (Es.

says on the Intellectual Poxvers, p. 530, 4to edition.) In both of

these instances, and, indeed, in the general strain of argument

Avliichruns through his works, he understands cojmnon sense in its

ordinary acceptation, as synonymous, or very nearly synonymous,

with the word reason, as it is now most frequently employed. In

n few cases, however, he seems to have annexed to the same

phrase a technical meaning of his own, and has even spoken of

this meaning as a thing not generally understood. Thus, after

illustrating the different classes oi natural signs, he adds the fol-

lowing sentence :" It may be observed, that as the first class of

*' natural signs I have mentioned is the foundation of true philo-

" sophy, and the second of the fine arts or of taste, so the last is

" the foundation of co?»/HOrt sense ; a part of human 7iature which

*' hath never been explained."—Inquiry, Chap. v. Sect. 3.

Sec Note (D.)


have in general been classed togetlier as partlzans of

a new sect, and as mutually responsible for the doc-

trines of each other. It is easy to perceive the use

likely to be made of this accident by an uncandid

antagonist.

All of these writers have, in my opinion, been

occasionally misled in their speculations, by a want

of attention to the distinction between first principles,

properly so called, and the fundamental laws of hu-

man belief. Buffier himself has fallen into the same

error ; nor do I know of any one logician, from the

time of Aristotle downwards, who has entirely avoid-

ed it.

The foregoing critical remarks will, I hope, have

their use in keeping this distinction more steadily

in the view of future inquirers ; and in preventing

some of the readers of the publications to which they

relate from conceiving a prejudice, in consequence

of the looseness of that phraseology which has been

accidentally adopted by their authors, against the

just and important conclusions which they contain.

94) ELEMENTS OF THE PHILOSOPHY Chap. II.

CHAPTER SECOND.

OF REASONING AND OF DEDUCTIVE EVIDENCE.

Section I.

Doubts mth respect to Locke's Distinction between

the Powers of Intuition and of Reasoning.

Although, in treating of this branch of the Philo-

sophy of the Mind, I have followed the example of

preceding writers, so far as to speak of Intuition and

Reasoning as two different faculties of the under-

standing, I am by no means satisfied that there ex-

ists between them that radical distinction which is

commonly apprehended. Dr Beattie, in his Essay

on Truth, has attempted to shew, that, how closely

soever they may in general be connected, yet that this

connection is not necessary ; insomuch, that a being

may be conceived endued with the one, and at the

same time destitute of the other.* Something of

this kind, he remarks, takes place in dreams and in

madness ; in both of which states of the system, the

power of Reasoning appears occasionally to be retain-

ed in no inconsiderable degree, while the power of

* Rcattie's Essay, p. 41, 2d edit.


Intuition is suspended or lost. But this doctrine is

liable to obvious and to insurmountable objections ;

and has plainly taken its rise from the vagueness of

the phrase common sense, which the author employs

through the whole of his argument, as synonymous

with the power of mtuition. Of the indissoluble

connection between this last power and that of rea-

soning, no other proof is necessary than the follow-

ing consideration, that, " in every step which rea-

" son makes in demonstrative knowledge, there

*' must be intuitive certainty ;'* a proposition which

Locke has excellently illustrated, and which, since

his time, has been acquiesced in, so far as I know,

by philosophers of all descriptions. From this pro-

position (which, wîen properly interpreted, appears

to me to be perfectly just) it obviously follows, that

the power of reasoning presupposes the power of in-

tuition ; and, therefore, the only question about

which any doubt can be entertained is. Whether the

power of Intuition (according to Locke's idea of it)

does not also imply that of reasoning ? My own

opinion is, decidedly, that it does ; at least, when

combined with the faculty of Memory. In examin-

ing those processes of thought which conduct the

mind by a series of consequences from premises to a

conclusion, I can detect no intellectual act what-

ever, which the joint operation of intuition and of

memory does not sufficiently explain.

Before, however, proceeding farther in this dis-

cussion, it is proper for me to observe, by way of

comment on the proposition just quoted from Locke,

that, although, <' in a complete demonstration, there

96 ELEMENTS OF THE PHILOSOPHY Chap. II.

" must be intuitive evidence at every step," it is not

to be supposed, that, in every demonstration, all the

various intuitive judgments leading to the conclu-

sion are actually presented to our thoughts. In by

far the greater number of instances, we trust entire-

ly to judgments resting on the evidence of memory ;

by the help of which faculty, we are enabled to con-

nect together the most remote truths, with the very

same confidence as if the one were an immediate

consequence of the other. Nor does this diminish,

in the smallest degree, the satisfaction we feel in fol-

lowing such a train of reasoning. On the contrary,

nothing can be more disgusting than a demonstra-

tion where even the simplest and most obvious steps

are brought forward to view ; and where no appeal

is made to that stock of previous knowledge which

memory has identified with the operations of reason.

Still, however, it is true, that it is by a continued

chain of intuitive judgments, that the whole science

of geometiy hangs together ; inasmuch as the de-

monstration of any one proposition virtually includes

all the previous demonstrations to which it refers.

Hence it appears, that, in mathematical demon-

strations, we have not, at every step, the immediate

evidence of intuition, but only the evidence of me-

mory. Every demonstration, however, may be re-

solved into a series of separate judgments, either

formed at the moment, or remembered as the results

ofjudgments formed at some preceding period ; and

it is in the arrangement and concatenation of these

different judgments, or media of proof, that the in-

u

Sect. 1

.

OP THE HUMAN MIND. 97

ventive and reasoning powers of the mathematician

find so noble a fiehl for their exercise.

Witli respect to these powers of judgment and of

reasoning, as they are here combined, it appears to

nie, that the results of the former may be compared

to a collection of separate stones prepared by the

chisel for the purposes of the builder ; upon each of

which stones, while lying on the ground, a person

may raise himself, as upon a pedestal, to a small ele-

vation. The same judgments, when combined into

a train of reasoning, terminating in a remote con-

clusion, resemble the formerly unconnected blocks,

when converted into the steps of a staircase leading

to the summit of a tower, which would be otherwise

inaccessible. In the design and execution of this

staircase, much skill and invention may be display-

ed by the architect ; but, in order to ascend it, no-

thing more is necessary than a repetition of the act

by which the first step was gained. The fact I con-

ceive to be somewhat analogous, in the relation be-

tween the power of judgment, and what logicians

call the discursive processes of the understanding.

Mr Locke's language, in various parts of his

Essay, seems to accord with the same opinion.

" Every step in reasoning," he observes, " that pro-

" duces knowledge, has intuitive certainty ; which,

" xvhen the mind perceives, there is ?io morê re-

" quired but to remember it, to make the agreement

" or disagreement of the ideas, concerning which

" we inquire, visible and certain. This intuitive

** perception of the agreement or disagreement of

VOL. II. G


** the intermediate ideas, in each step and progres-

" sion of the demonstration, must also be carried ex-

** actly in the mind, and a man must be sure that no" part is left out ; which, in long deductions, and

" in the use of many proofs, the memory does not

** always so readily and exactly retain : therefore it

" comes to pass, that this is more imperfect than in-

" tuitive knowledge, and men embrace often false-

*' hood for demonstrations." *

The same doctrine is stated elsewhere by MrLocke, more than once, in terms equally explicit ; t

and yet his language occasionally favours the sup-

position, that, in its deductive processes, the mind

exhibits some modification of reason essentially dis-

tinct from intuition. The account, too, which he

has given of their respective provinces, affords evi-

dence that his notions concerning them were not

sufficiently precise and settled. ** When the mind,"

says he, " perceives the agreement or disagreement

*' of two ideas immediately by themselves, without

** the intervention of any other, its knowledge may" be called intuitive. When it cannot so bring

" its ideas together as, by their immediate compari-

" son, and, as it were, juxta-position, or application

" one to another, to perceive their agreement or dis-

" agreement, it is fain, by the intervention of other

" ideas (one or more, as it happens), to discover the

" agreement or disagreement which it searches ; and

" this is that which we call reasoningJ* t Accord-

* B. IV. Chap. ii. § 7- See also B. IV. Chap. xvii. § 15.

t B. IV. Chap. xvii. § 2. B. IV. Chap. xvii. § 4. § 14.

I B. IV. Chap. ii. §§ Land 2.


ing to these definitions, supposing the equality of

two lines A and B to be perceived immediately in

consequence of their coincidence ; the judgment of

the mind is intuitive : Supposing A to coincide with

B, and B with C ; the relation between A and Cis perceived by reasoning. Nor is this a hasty in-

ference from Locke's accidental language. That it

is perfectly agreeable to the foregoing definitions, as

understood by their author, appears from the follow-

ing passage, which occurs afterwards : " The prin-

" cipal act of ratiocination is the finding the agree-

" ment or disagreement of two ideas, one with an-

" other, by the intervention of a third. As a man,

*' by a yard, finds two houses to be of the same*' length, which could nOt be brought together to

" measure their equality by juxta-position.** *

This use of the words intuition and reasoning is

surely somewhat arbitrary. The truth of mathema-

tical axioms has always been supposed to be intui-

tively obvious ; and the first of these, according to

Euclid's enumeration, affirms, That if A be equal

to B, and B to C, A and C are equal. Admitting,

however, Locke's definition to be just, it only tends

to confirm what has been already stated with respect

to the near affinity, or rather the radical identity, of

intuition and of reasoning. Wlien the relation of

equality between A and B has once been perceived,

A and B are completely identified as the same ma-

thematical quantity ; and the two letters may be

regarded as synonymous wherever they occur. The

* B. IV. Chap. xvii. § 18.

100 ELEMENTS OP THE PHILOSOPHY Chap. II.

faculty, therefore, which perceives the relation be-

tween A and C, is the same with the faculty which

perceives the relation between A and B, and between

B and C*In farther confirmation of the same proposition,

an appeal might be made to the structure of syllogisms.

Is it possible to conceive an understanding so form-

ed as to perceive the truth of the major and of the

minor propositions, and yet not to perceive the force

of the conclusion ? The contrary must appear evi-

dent to every person who knows what a syllogism

is ; or rather, as in this mode of stating an argu-

ment, the mind is led from universals to particulars,

it must appear evident, that, in the very statement

of the major proposition, the truth of the conclusion

is presupposed ; insomuch, that it was not without

good reason Dr Campbell hazarded the epigram-

matic, yet unanswerable remark, that *' there is al-

" ways some radical defect in a syllogism, which is

*' not chargeable with that species of sophism known" among logicians by the name of petitio pincipHj

" or a begging of the question.** \

* Dr Reid's notions, as well as those of Mr Locke, seem to

have been somewhat unsettled with respect to the precise line

which separates intuition from reasoning. 'I'hat the axioms of

geometry are intuitive truths, he has remarked in numberless

passages of his works ; and yet, in speaking of the application

of the syllogistic theory to mathematics, he makes use of the

following expression :" The simple reasoning., ' A is equal to B,

" and B to C, therefore A is equal to C,' cannot be brought into

" any syllogism in figure and mode.*'—See his Analysis of

Aristotle's Logic.

i Phil. ofRhet. Vol. I. p. 174.


The idea which is commonly annexed to intuilio?iy

as opposed to reasoning, turns, I suspect, entirely

on the circumstance of time. The former we con-

ceive to be instantaneous ; whereas the latter neces-

sarily involves the notion of succession, or of pro-

gress. This distinction is sufficiently precise for

the ordinary purposes of discourse ; nay, it supplies

us, on many occasions, with a convenient phraseo-

logy : but, in the theory of the mind, it has led

to some mistaken conclusions, on which I intend

to offer a few remarks in the second part of this

section.

So much with respect to the separate provinces

of these powers, according to Locke ;—a point on

which I am, after all, inclined to think, that myown opinion does not differ essentially from his,

whatever inferences to the contrary may be drawn

from some of his casual expressions. The mis-

apprehensions into which these have contributed to

lead various writers of a later date, will, I hope,

furnishâ sufficient apology for the attempt which I

have made, to place the question in a stronger

light than he seems to have thought requisite for its

illustration.

In some of the foregoing quotations from his

Essay, there is another fault of still greater moment

;

of which, although not immediately connected with

the topic now under discussion, it is proper for meto take notice, that I may not have the appearance

of acquiescing in a mode of speaking so extremely

exceptionable. A\liat I allude to is, the supposition

which his language, concerning the powers both of


intuition and of reasoning, involves, that knowledge

consists soleli/ in the perception of the agreement or

the disagreement ofour ideas. The impropriety of

this phraseology has been sufficiently exposed by DrReid, whose animadversions I would beg leave to

recommend to the attention of those readers, who,

from long habit, may have familiarized their ear to

the peculiarities of Locke's philosophical diction.

In this place, I think it sufficient for me to add to

Dr Reid's strictures, that Mr Locke's language has,

in the present instance, been suggested to him by

the partial view which he took of the subject ; his

illustrations being chiefly borrowed from mathe-

matics, and the relations about which it is conver-

sant. Wlien applied to these relations, it is un-

doubtedly possible to annex some sense to such

phrases as comparing ideas^—the jiuta-position of

ideas,—the perception of the agreements or dis-

agreements of ideas ; but, in most other branches

of knowledge, this jargon will be found, on examina-

tion, to be altogether unmeaning ; and, instead of

adding to the precision of our notions, to involve

plain facts in technical and scholastic mystery.

This last observation leads me to remark farther,

that even when Locke speaks of reasoning in gene-

ral, he seems, in many cases, to have had a tacit

reference, in his own mind, to mathematical demon-

stration ; and the same criticism may be extended

to every logical writer whom I know, not excepting

Aristotle himself. Perhaps it is chiefly owing to

this, that their discussions are so often of very

little practical utility ; the rules which result from

11


them being wholly superfluous, when applied to

mathematics ; and, when extended to other branch-

es of knowledge, being unsusceptible of any pre-

cise, or even intelligible interpretation.

II.

Condusioiis obtained hy a Process of Deduction

often mistakenfor Intuitive Judgments.

It has been frequently remarked, that the justest

and most efficient understandings are often posses-

sed by men who are incapable of stating to others,

or even to themselves, the grounds on which they

proceed in forming their decisions. In some in-

stances, I have been disposed to ascribe this to the

faults of early education ; but, in other cases, I ampersuaded, that it was the effect of active and impe-

rious habits in quickening the evanescent processes

of thought, so as to render them untraceable by the

memory ; and to give the appearance of intuition

to what was in fact the result of a train of reasoning

so rapid as to escape notice. This I conceive to be

the true theory of what is generally called common

sense, in opposition to book-learning ; and it serves

to account for the use which has been made of this

phrase, by various writers, as synonymous with in-

tuition.

These seemingly instantaneous judgments have al-

ways appeared to me as entitled to a greater share

of our confidence than many of our more deliberate

conclusions 5 inasmuch as they have beenforced, as

104 ELEMENTS OF THE PHILOSOPHY Cliap. 11.

it were, on the mind by the lessons of long expe-

rience ; and are as little liable to be biassed by tem-

per or passion, as the estimates we form of the dis-

tances of visible objects. They constitute, indeed,

to those who are habitually engaged in the busy

scenes of life, a sort of peculiar facidhj, analogous,

both in its origin and in its use, to the coup (Toeil

of the military engineer, or to the quick and sure

tact of the medical practitioner, in marking the di-

agnostics of disease.

For this reason, I look upon the distinction be-

tween our intuitive and deductive judgments as, in

many cases, merely an object of theoretical curiosity.

In those simple conclusions which all men are im-

pelled to form by the necessities of their nature, and

in which we find an uniformity not less constant

than in the acquired perceptions of sight, it is of as

little consequence to the logician to spend his time

in efforts to retrace the first steps of the infant un-

derstanding, as it would be to the sailor or the

sportsman to study, with a view to the improvement

of his eye, the Berkeleian theory of vision. In both

instances, the original faculty and the acquired

judgment are equally entitled to be considered as

the work of Nature ; and in both instances we find

it equally impossible to shake off her authority. It

is no wonder, therefore, that, in popular language,

such words as commo7i sense and reason should be

used with a considerable degree of latitude ; nor is

it of much importance to the philosopher to aim at

extreme nicety in defining their province, where ail

4


mankind, whether wise or ignorant, think and speak

alike.

In some rare and anomalous cases, a rapidity of

judgment in the more complicated concerns of life,

appears in individuals who have had so few opportu-

nities of profiting by experience, that it seems, on a

superficial view, to be the immediate gift of heaven.

But, in all such instances (although a great deal ;^

must undoubtedly be ascribed to an inexplicable ap- >4,

titude or predisposition of the intellectual powers),

we may be perfectly assured, that every judgment

of the understanding is preceded by a process of rea-

soning or deduction, whether the individual him-

self be able to recollect it or not. Of this I can no

more doubt, than I could bring myself to believe

that the Arithmetical Prodigy, who has, of late, so

justly attracted the attention of the curious, is able

to extract square and cube roots by an instinctive

and instantaneous perception, because the process

of mental calculation, by which he is led to the re-

sult, eludes all his efforts to recover it.*

It is remarked by Mr Hume, with respect to the

elocution of Oliver Cromwell, that " it was al*

" ways confused, embarrassed, and unintelligible."

—" The great defect, however," he adds, " in Oli-

*' ver's speeches, consisted, not in his want of elocu-

" tion, but in his want of ideas ; the sagacity of his

** actions, and the absurdity of his discourse, form-

" ing the most prodigious contrast that ever was" known."—*' In the great variety of human ge-

* See Note (E.)


" niuses," says the same historian, upon a different

occasion, " there are some which, though they see

^ *' their object clearly and distinctly in general; yet,

" when they come to unfold its parts by discourse or

** writing, lose that luminous conception which they

" had before attained. All accounts agree in as-

" cribing to Cromwell a tiresome, dark, unintelli-

" gible elocution, even when he had no intention to

" disguise his meaning : Yet, no man's actions were

** ever, in such a variety of difficult incidents, more

" decisive and judicious."

The case here described may be considered as an

extreme one ; but every person in common obser-

vation must recollect facts somewhat analogous,

which have fallen under his own notice. Indeed,

it is no more than we should expect a priori to

meet with, in every individual whose early habits

have trained him more to the active business of the

world, than to those pursuits which prepare the

mind for communicating to others its ideas and feel-

incrs with clearness and effect.

An anecdote which I heard, many years ago, of

a late very eminent Judge (Lord Mansfield), has of-

ten recurred to my memory, while reflecting on

these apparent inconsistencies of intellectual charac-

ter. A friend of his, who possessed excellent na-

tural talents, but who had been prevented, by his

professional duties as a naval officer, from bestowing

on them all the cultivation of which they were sus-

ceptible, having been recently appointed to the go-

vernment of Jamaica, happened to express some

doubts of his competency to preside in the Court of


Chanceiy. Lord Mansfield assured hnn, that he

would find the difficulty not so great as he appre-

hended. " Trust," he said, " to your own good

" sense in fonning your opinions ; but beware of at-

" tempting to state the grounds of your judgments.

" The judgment will probably be right ;—^the argu-

" ment will infallibly be wrong."

From what has been said, it seems to follow, that

although a man should happen to reason ill in sup-

port of a sound conclusion, we are by no means en-

titled to infer, with confidence, that he judged right,

merely by accident. It is far from being impossible

that he may have committed some mistake in stat-

ing to others (perhaps in retracing to himself) the

grounds upon which his judgment was really found-

ed. Indeed, this must be the case, wherever a

shrewd understanding in business is united with an

incapacity for clear and luminous reasoning ; and

something of the same sort is incident, more or less,

to all men (more particularly to men of quick parts)

when they make an attempt, in discussions concern-

ing human affairs, to remount toJirst principles. It

may be added, that in the old, this correctness of

judgment often remains, in a surprising degree,

long after the discursive or argumentative power

would seem, from some decay of attention, or con-

fusion in the succession of ideas, to have been sensi-

bly impaired by age or by disease.

In consequence of these views, as well as of va-

rious others foi'eign to the present subject, I am led to

entertam great doubts about the solidity of a very

specious doctrine laid down by Condorcet, in his


" Essay on the Application of Mathematical Analy-

" sis to the Probabilities of Decisions resting upon

*' the Votes of a Majority." *' It is extremely pos-

" sible,'* he observes, *' that the decision which

" unites in its favour the greatest number of suffrages,

" may comprehend a variety of propositions, some

** of which, if stated apart, would have had a plura-

" lity of voices against them ; and, as the truth of a

" system of propositions, supposes that each of the

" propositions composing it is true, the probability of

" the system can be rigorously deduced only from

" an examination of the probability of each proposi-

" tion, separately considered." *

When this theory is applied to a court of law, it

is well known to involve one of the nicest questions

in practical jurisprudence ; and, in that light, I do

not presume to have fonned any opinion with respect

to it. It may be doubted, perhaps, if it be not one

of those problems, the solution of which, in particu-

lar instances, is more safely entrusted to discretion-

ary judgment, than to the rigorous application of

any technical rule founded on abstract principles. I

have introduced the quotation here, merely on ac-

count of the proof which it has been supposed to af-

ford, that the seeming diversities ofhuman belief fall,

in general, greatly short of the reality. On this

* Essai sur I'Application de I'Analyse aia probabilite des De-

cisions rcndues h la pluralite des Voix.

—

Disc. Prel. pp. 4-6, 47-

Some of the expressions in the above quotation are not agree-

able to the idiom of our language ; but I did not think myself en-

titled to depart from the phraseology of the original. The mean-

ing is sufhciently obvious*


point, the considerations already stated strongly in-

cline me to entertain an idea directly contrary. Myreasons for thinking so may be easily collected from

the tenor of the preceding remarks.

It is time, however, to proceed to the examination

of those discursive processes, the different steps of

which admit of being distinctly stated and enunci-

ated in the form of logical arguments ; and which,

in consequence of this circumstance, furnish more

certain and palpable data for our speculations. I

bea'in with some remarks on the Power of General

Reasoning ; for the exercise of which (as I fonner-

ly endeavoured to shew), the use of language, as an

instrument of thought, is indispensably requisite.

Section II.

Of General Reasomig*

I.

Illustrations of some Remarks formerly stated in

treating ofAbstraction,

I SHOULD scarcely have thought it necessary to

resume the consideration of Abstraction here, if I

had not neglected, in my first volume, to examine

the force of an objection to Berkeley's doctrine con-

cerning abstract general ideas, on which great stress

is laid by Dr Reid, in his Essays on the Intellectual

Powers of Man j and which some late writers seem

to have considered as not less conclusive against the

view of the question which I have taken. Of this


objection I was aware from the first ; but was un-

willing, by replying to it in form, to lengthen a dis-

cussion which savoured so much of the schools;

more especially, as I conceived that I had guarded

my own argument from any such attack, by the

cautious tenns in which I had expressed it. Hav-

ing since had reason to believe that I was precipitate

in forming this judgment, and that Reid's strictures

on Berkeley's theory of General Signs have produ-

ced a deeper impression than I had expected, * I

shall endeavour to obviate them, at least as far as

they apply to myself, before entering on any new spe-

culations concerning our reasoning powers ; and

shall, at the same time, introduce some occasional

illustrations of the principles which I formerly en-

deavoured to establish.

To prevent the possibility of misrepresentation, I

state Dr Reid*s objection in his own words.

" Berkeley, in his reasoning against abstract ge-

" neral ideas, seems unwillingly or unwaringly to

" grant all that is necessary to support abstract and

" general conceptions.

*' A man," says Berkeley, " may consider a fi-

" gure merely as triangular, without attending to

*' the particular qualities of the angles, or relations

*' of the sides. So far he may abstract. But this

* See a book entitled, Elements of Intellectual Philosophy,

by the late learned and justly regretted Mr Scott, of King's Col-

lege, Aberdeen, p. 118, et seq. (Edinburgh, 1805.) I have not

thought it necessary to reply to Mr Scott's own reasonings,

which do not appear to me to throw much new light on the ques-

tion ; but I thought it right to refer to them here, that the reader

may, if he pleases, have an opportunity of judging for himself.

Sect. 2. OF THE HUÎAN MIND. Ill

" will never prove that he can frame an abstract ge-

" neral inconsistent idea of a triangle.'*

Upon this passage Dr Reid makes the following

remark : "Ifci man may C07isidcr afigure merely** as triangulary he must have some conception of" tlus object of his consideration ; for no man can

" consider a thing 'which he does not conceive. He** has a conceptio7if therefore, ofa triangidarfigure,

" merely as such. I know no more that is meant** by an abstract general conception ofa triangle.*'

*' He that considers a figure merely as triangu-

" lar," continues the same author, " must under-

*' stand what is meant by the word triangular. If

** to the conception he joins to this word, he adds

" any particular quality of angles or relation of sides,

*' he misunderstands it, and does not consider the

" figure merely as triangular. Whence I think it is

" evident, that he who considers a figure merely as

*• triangular, must have the conception of a triangle,

" abstracting from any quality of angles or relations

« of sides." *

For what appears to myself to be a satisfactory an-

swer to this reasoning, I have only to refer to the

first volume of these Elements. The remarks to

which I allude are to be found in the third section of

chapter fourth j t and I must beg leave to recom-

mend them to the attention of my readers, as a ne-

cessary preparation for the following discussion.

In the farther prosecution of the same arguirient,

Dr Reid lays hold of an acknowledgment tvhich

* Reid's Intellectual Powers, p. 4S3, 4to edit.

t P. 195, 3d edit.

112 ELEMENTS OF THE PHILOSOPHY Chap. 11.

Berkeley has made, *' That we may consider Peter

" so far forth as man, or so far forth as animal, in-

" asmuch as all that is perceived is not considered.'*

—" It may here,** says Reid, " be observed, that

" he who considers Peter so far forth as man, or so

*' flu* forth as animal, must conceive the meaning of

" those abstract general words 7nan and animal

;

" and he who conceives the meaning of them, has an

" abstract general conception.'*

According to the definition of the word concejJ-

tion^ which I have given in treating of that faculty

of the mind, a general conception is an obvious im-

possibility. But, as Dr Reid has chosen to annex a

more extensive meaning to the term than seems to

me consistent with precision, I would be far from

being understood to object to his conclusion, mere-

ly because it is inconsistent with an arbitrary defini-

tion of my own. Let us consider, therefore, how

far his doctrine is consistent with itself j or rather,

since both parties are evidently so nearly agreed

about the principal fact, which of the two have adopt-

ed the more perspicuous and philosophical mode of

stating it.

In the first place, then, let it be remembered as

a thing admitted on both sides, " that we have a

" power of reasoning concerning a figure consider-

" ed merely as triangular, without attending to the

" particular qualities of the angles, or relations of

" the sides ;'* and also, that " we may reason con-

** cerning Peter or Johrif considered so far forth as

** mant or so far forth as atmial." About these

facts there is but one opinion j and the only ques-

Sect. 2. <5F THE HUMAN MIND. 1 13

tion is, A^Tiether it throws additional light on the

subject, to tell us, in scholastic language, that " we

" are enabled to carry on these general reasonings,

" in consequence of the power which the mind has

** of forming abstract general conceptions." To

myself it appears, that this last statement (even on

the supposition that tiie word co?icepfion is to be un-

derstood agreeably to Dr Reid's own explanation)

can serve no other purpose than that of involving a

plain and simple truth in obscurity and mystery.

If it be used in the sense in which I have invariably

employed it in this work, the proposition is altoge-

ther absurd and incomprehensible.

For the more complete illustration of this point, I

must here recur to a distinction formerly made be-

tween the abstractions which are subservient to rea-

soning, and those which are subservient to imagina-

tion. *' In every instance in which imagination is

" employed in forming new wholes, by decompound-

" ing and combining the perceptions of sense, it is

" evidently necessary that the poet or the painter

" should be able to state or represent to himself the

" circumstances abstracted, as separate objects of

" conception. But this is by no means requisite in

" every case in which abstraction is subservient to

** the power of reasoning ; for it frequently hap-

" pens, that we can reason concerning the quality

" or property of an object abstracted from the rest,

*' while, at the same time, we find it impossible to

*' conceive it separately. Thus, I can reason con-

** cerning extension and figure, without any refe-

VOL. II. H

114} ELEMENTS OF THE PHILOSOPHY Chap. 11.

** rence to colour, although it may be doubted, if a

" person possessed of sight can make extension and

" figure steady objects of conception, without con-

** necting with them the idea of one colour or ano-

*' ther. Nor is this always owing (as it is in the in-

*' stance just mentioned) merely to the association of

" ideas ; for there are cases, in which we can reason

" concerning things separately, which it is impossi-

" ble for us to suppose any mind so constituted as to

" conceive apart. Thus, we can reason concerning

" length, abstracted from any other dimension ; al-

" though, surely, no understanding can make length,

" without breadth, an object of conception.'* * In

like manner, while I am studying Euclid's demon-

stration of the equality of the three angles of a tri-

angle to two right angles, I find no difficulty in fol-

lowing his train of reasoning, although it has no re-

ference whatever to the specific size or to the speci-

fic Jbr7n of the diagram before me. I abstract.,

therefore, in this instance, from both of these cir-

cumstances presented to my senses by the immedi-

ate objects of my perceptions ; and yet it is mani-

festly impracticable for me either to delineate on

paper, or to conceive in the mind, such a figure as

shall not include the circumstances from which I ab-

stract, as well as those on which the demonstration

hinges.

In order to fonn a precise notion of the manner

in which this process of the mind is carried on, it is

necessary to attend to the close and inseparable con-

* Vol. I. pp. 157, 158, 3d edif.

Sect.?. OF THE HUMAN MIND. 116

iiection which exists between the faculty of general

reasoning, and the use of artificial language. It is

in consequence of the aids which this lends to our

natural faculties, that we are furnished with a class

of signs, expressive of all the circumstances which

we wish our reasonings to comprehend ; and, at the

same time, exclusive of all those which we wish to

leave out of consideration. The word triangle, for

instance, when used without any additional epithet,

confines the attention to the three angles and three

sides of the figure before us ; and reminds us, as we

proceed, that no step of our deduction is to turn on

any of the specific varieties which that figure may

exhibit. The notion, however, which we annex to

the word triangle, while we are reading the demon-

stration, is not the less a particular notion, that

this word, from its partial or abstracted import, is

equally applicable to an infinite variety of other in-

dividuals. *

* *' By this imposition of names, some of larger, some of strict-

*' or signilicadon, wc turn the reckoning of the consequences of

" things imagined in the mind, into a reckoning of the conse-

*' quences of appellations. For example, a man that hath no" use of speech at all (such as is born and remains perfectly deaf

" and dumb), if he set before his eyes a triangle, and by it two" right angles (such as are the corners of a square figure), he

" may by meditation compare and find, that the three angles of

" that triangle are equal to those right angles that stand by it.

" But if anuther triangle be shewn him, different in shape from

" the former, he cannot know, without a new labour, whether

" the three angles of that also be equal to the same. But he" that hath the use of words, when he observes that such equa-

" lity -was consequent, not to the length of the sides, nor to any

il6 ELEMENTS OF THE PHILOSOPHY Chap. II.

These observations lead, in my opinion, to so

easy an explanation of the transition from particular

to general reasoning, that I shall make no apology

for prosecuting the subject a little farther, before

leaving this branch of my argument.

It will not, I apprehend, be denied, that when a

learner first enters on the study of geometiy, he con-

siders the diagrams before him as individual objects,

and as individual objects alone. In reading, for ex-

ample, the demonstration just referred to, of the

equality of the three angles of every triangle to two

right angles, he thinks only of the triangle which is

presented to him on the margin of the page. Nay,

so completely does this particular figure engross his

attention, that it is not without some difficulty he, in

the first instance, transfers the demonstration to an-

other triangle whose form is very different, or even

to the same triangle placed in an inverted position.

It is in order to correct this natural bias of the mind,

that a judicious teacher, after satisfying himself that

the student comprehends perfectly the force of the

*' pai'ticular thing in this triangle; but only to this, that the

" sides were straight, iind the angles three ; and that that was all

*' for which he named it a triangle ; will^ boldly conclude uni-

*' versally, that such equality ol angles is in all triangles whatso-

" ever, and register his invention in these general terms, Every

" triangle hath its three a/igi'es equal to two right angles. And** thus the consequence foun i iii one particular, comes to be re-

*' gistered and remenibt red as an universal rule ; and discharges

*' our mental reckoning of time and place ; and delivers us from

'' all labour of the mind, saving the first ; and makes that which

*' was found true here, and ?iow, to betrueinc// times and places,"

^Hobbcs, Of Man, Part I. Chap. iv.


demonstration, as applicable to the particular triangle

which Euclid has selected, is led to vary the diagram

in different ways, with a view to shew him, that the

veiy same demonstration, expressed in the very same

form of words, is equally applicable to them all. In

this manner he comes, by slow degrees, to compre-

hend the nature of general reasoning, establishing

insensibly in his mind this fundamental logical prin-

ciple, that when the enunciation of a mathematical

proposition involves only a certain portion of the at-

tributes of the diagram which is employed to illus-

trate it, the same proposition must hold true of any

other diagram involving the same attributes, how

much soever distinguished from it by other speci-

fic peculiarities. *

* In order to impress the mind still more forcibly with the

same conviction, some have supposed that it might be useful, in

an elementary work, such as that of Euclid, to omit the diagrams

altogether, leaving the student to delineate them for himself^

agreeably to the terms of the enunciation and of the construction.

And were the study of geometry to be regarded merely as subser-

vient to that of logic, much might be alleged in confirmation of

this idea. Where, however, it is the main purpose of the teacher

(as almost always happens) to familiarize the mind of his pupil

with the fundamental principles of the science, as a preparation

for the study of physics and of the other parts of mixed mathe-

juatics, it cannot be denied, that such a practice would be far

less favourable to the memory than the plan which Euclid has

adopted, of annexing to each theorem an appropriate diagram,

with which the general truth comes very soon to be strongly as-

sociated. Nor is this circumstance found to be attended in prac-

tice with the inconvenience it may seem to threaten ; inasmuch

as the student, without any reflection whatever on logical princi-

ples, generalizes the particular example, according to the differ-

118 ELEMENTS OF THE PHILOSOPHY Chap. II-

Of all the generalizations in geometry, there are

none into which the mind enters so easily, as those

which relate to diversities in point of size or mag?!}-

tude. Even in reading the very first demonstrations

of Euclid, the learner almost immediately sees, that

the scale on which the diagram is constructed, is as

completely out of the question as the breadth or the

colour of the lines which it presents to his external

senses. The demonstration, for example, of the

fourth proposition, is transferred, without any con-

scious process of reflection, from the two triangles on

the margin of the page, to those comparatively large

ones which a public teacher exhibits on his board or

slate to a hundred spectators. I have frequently,

ent cases which may occur, as easily and unconsciously as he

could have applied to these cases the general enunciation.

The same remark may be extended to the other departments of

i our knowledge ; in all of which it will be found useful to asso-

* ciate^with every important general conclusion some particular ex-

ample or illustration, calculated, as much as possible, to present

an imp:essive image to the power of conception. By this means,

while the example gives us a firmer hold and a readier command

of the general theorem, the theorem, in its turn, serves to correct

the errors into which the judgment might be led by the specific

peculiaritiesiof the example. Hence, by the way, a strong argu-

ment in favour of the practice recommended by Bacon, of con-

necting emblems with prccnotions, as the most powerful of all ad-

minicles to the faculty of memory; and hence the aid which this

faculty may be expected to receive, in point of promptitude, if

not of correctness, from a lively imagination. Nor is it the least

advantage of this practice, that it supplies us at all times with

ready and apposite illustrations to facilitate the communication

of our general conclusions to others. But the prosecution of

these hints would lead me too far astray from the subject of this

section. 4

Sect. '2. OF THE HUMAN MIND. 119

however, observed in beginners, while employed in

copying such elementary diagrams, a disposition to

make the copy, as nearly as possible, both in size and

figure, a Jac simile of the original.

The generalizationswhich extend to varieties o^form

and 0^ position^ are accomplished much more slowly ;

and, for this obvious reason, that these varieties are

more strongly marked and discriminated ffom one

another, as objects of vision and of conception.

How difficult (comparatively speaking), in such in-

stances, the generalizing process is, appears mani-

festly from the embarrassment which students expe-

rience, in applying the fourth proposition to the de-

monstration of the fifth. The inverted position,

and the partial coincidence of the two little triangles

below the base, seem to render their mutual relation

so different from that of the two separate triangles

which had been previously fiimiliarized to the eye, that

it is not surprising this step of the reasoning should

be followed, by the mere novice, with some degree

of doubt and hesitation. Indeed, where nothing of

this sort is manifested, I should be more inclined to

ascribe the apparent quickness of his apprehension to

a retentive memory, seconded by implicit faith in his

instructor, than to regard it as a promising symp-

tom of mathematical genius.

Another, and perhaps a better illustration of that

natural logic which is exemplified in the generaliza-

tion of mathematical reasonings, may be derived

from those instances where the same demonstration

applies, in the same words, to what are called in geo-

metry the different cases of a proposition. In the


commencement of our studies, we read the demon-

stration over and over, applying it successively to

the different diagrams ; and it is not without some

wonder we discover, that it is equally adapted to

them all. In process of time, we learn that this la-

bour is superfluous ; and if we find it satisfactory in

one of the cases, can anticipate with confidence the

justness of the general conclusion, or the modifica-

tions which will be necessary to accommodate it to

the different forms of which the hypothesis may ad-

mit.

The algebraical calculus, however, when applied

to geometry, places the foregoing doctrine in a point

^f view still more striking; " representing," to bor-

. row the words of Dr Halley, " all the possible cases

" of a problem at one view ; and often in one gene-

" raltheoremcomprehending whole sciences; which,

" deduced at length into propositions, and demon-

" strated after the manner of the ancients, might

*' well become the subject of large treatises." * Ofthis remark, Halley gives an instance in 2iformula,

which, when he first published it, wâs justly regard-

ed " as a notable instance of the great use and com-

" prehensiveness of algebraic solutions." I allude

to his formula for finding universally the foci of op-

tic lenses ; an example which I purposely select, as

it cannot fail to be familiarly known to all who have

the slightest tincture of mathematical and physical

science.

In such instances as these, it will not surely be

* Philos. Transact. No. 205. Miscell. Cur. Vol, I. p. 348.

Sect. 2. OF THE HUMAN BUND. 121

supposed, that while we read the geometrical demon-

stration, or follow the successive steps of the alge-

braical process, our general conceptions embrace all

the various possible cases to which our reasonings ex-

tend. So veiy different is the fact, that the wide

grasp of the conclusion is discovered only by a sort

of subsequent induction ; and, till habit has famili-

arized us with similar discoveries, they never fail to

be attended with a certain degree of unexpected de-

light. Dr Halley seems to have felt this strongly

when the o^\acq\. formula already mentioned first

presented itself to his mind.

In the foregoing remarks, I have borrowed myexamples from mathematics, because, at the period

of life when we enter on this study, the mind has ar-

rived at a sufficient degree of maturity to be able to

reflect accurately on every step of its own progress

;

whereas, in those general conclusions to which we

have been habituated from childhood, it is quite im-

possible for us to ascertain, by any direct examina-

tion, what the processes of thought were, which ori-

ginally led us to adopt them. In this point of view,

the first doubtful and' unassured steps of the young

geometer, present to tlie logician a peculiarly inte-

resting and instructive class Qf phenomena, for illus-

trating the growth and developement ofour reasoning-

powers. The true theory, more especially oi gene-

ral reasoning, may be here distinctly traced by

every attentive observer ; and may hence be confi-

dently applied (under due limitations) to all the

other departments of human knowledge. *

* The view of general reasoning which is given above, appears

1^2 ELEMENTS OF THE PHILOSOPHY Chap. II.

From what has been now said, it would appear,

that, in order to arrive at a general conclusion in

to myself to afibrd (without any comment) a satisfactory answer

to the following argument of the late worthy and learned Dr

Price :" That the universality consists in the idea, and not mere-

" ly in the name, as used to signify a number of particulars, rc-

" sembling that which is the immediate object of reflection, is

" plain; because, was the idea to which the name answers, and

" which it recals into the mind, only a particular one, we could

" not know to what other ideas to apply it, or what particular

" objects had the resemblance necessary to bring them within the

" meaning of the name. A person, in reading over a mathema-

" tical demonstration, certainly is conscious that it relates to

" somewhat else, than just that precise figure presented to him in

" the diagram. But if he knows not what else, of what use can

" the demonstration be to him i* How is his knowledge enlarged

" by it? Or how shall he know afterwards to what to apply it?"

In a note upon this passage, Dr Price observes, that, •' accord-

" ing to Dr Cudworth, abstract ideas are implied in the cognosci-

" tive power of' the mind ; which^ he says, contains in itself virtually

" (as thefuture plant or tree is contained in the seed) general «o-

" tions or exemplars of all things, which are exerted hy it, or iinfold

" and discover themselves^ as occasions invite, and proper circtim-

" stances occur." " Thi^, no doubt," Dr Price adds, " many will

" very freely condemn as whimsical and extravagant. I have, I

" own, a different opinion of it; but yet I should not care to be

'* obliged to defend it."

—

Review ofthe Principal Questions in Mo-

rals, pp. 38, 39, 2d edit.

For my own part, I have no scruple to say, that I consider this

fancy of Cudworth as not only whimsical and extravagant, but as

altogether unintelligible ; and yet it appears to me, that some

confused analogy of the same sort must exist in the mind of every

person who imagines that he has the power of forming general

conceptions without the intermediation of language.

In the continuation of the same note, Dr Price seems disposed

to sanction another remark of Dr Cudworth : in which he pro-

nounces the opinion of the nominaUsts to be so ridiculous andfalsct

^€Ct. 1'. OF THE HUMAN MIND. 123

mathematics (and the same observation holds with

respect to other sciences), two different processes of

reasoning are necessary. The one is the demon-

stration of the proposition in question ; in study-

ing which, we certainly think of nothing but the in-

dividual diagram before us. The other is, the train

of thought by which we transfer the particular con-

clusion to which we have been thus led, to any other

diagram to which the same enunciation is equally

applicable. As this last train of thought is, in all

cases, essentially the same, we insensibly cease to re-

peat it when the occasion for employing it occurs,

till we come at length, without any reflection, to

generalize our particular conclusion, the moment

it is formed ; or, in other words, to consider it as a

proposition comprehending an indefinite variety of

particular truths. When this habit is established,

we are apt to imagine,—forgetting the slow steps

by which the habit was acquired,—that the general

conclusion is an immediate inference from a general

demonstration ; and that, although there was only

one particular diagram present to our external senses,

we must have been aware, at every step, that our

thoughts were really conversant, not about this dia-

gram, but about general ideaSy or, in Dr Reid*s

as to deserve no confutation. I suspect, that when Dr Cudworth

wrote this splenetic and oracular sentence, he was out of humour

with some argument of Hobbes, which he found himself unable

to answer. It is not a little remarkable, that the doctrine which

he here treats with so great contempt, should, with a very few

exceptions, have united the suftrages of all the soundest philoso-

phers of the eighteenth century.

124 ELEMENTS OF THE PHILOSOPHY Chap. U.

language, general conceptions. Hence the familiar

use among logicians of these scholastic and myste-

rious phrases, which, whatever attempts may be

made to interpret them in a manner not altogether

inconsistent with good sense, have unquestionably

the effect of keeping out of view the real procedure

of the human mind in the generalization of its know-

ledge.

Dr Reid seems to be of opinion, that it is by the

power of fomiing general conceptions that man is

distinguished from the brutes ; for he observes, that

** Berkeley*s system goes to destroy the barrier

" between the rational and animal natures.** I

must own I do not perceive the justness of this re-

mark, at least in its application to the system of the

nominalists, as I have endeavoured to explain and

to limit it in the course of this work. On the con-

traiy, it appears to me, that the account which has

been just given of general reasoningy by ascribing

to a process of logical deduction (presupposing the

previous exercise of abstraction or analysis') what

Dr Reid attempts to explain by the scholastic, and

not very intelligible phrase of general conceptions^

places the distinction between man and brutes in a

far clearer and stronger light than that in which

philosophers have been accustomed to view it. That

it is to the exclusive possession of the faculty of

abstraction, and of the other powers subservient to

the use of general signs, that our species is chiefly

indebted for its superiority over the other animals, I

shall afterwards endeavour to shew.

It still remains for me to examine an attempt


which Dr Reid has made, to convict Berkeley of an

inconsistencj/t in the statement of his argument

against abstract general ideas. " Let us now consi-

" der,"sayshe, "the Bishop's notion ofgeneralizing.

** An idea (he tells us) which, considered in itself,

" is particular, becomes general, by being made to

" represent or stand for all other particular ideas of

*' the same sort. To make this plain by an example

:

** Suppose (says Berkeley) a geometrician is demon-

" strating the method of cutting a line into two

** equal parts. He draws, for instance, a black line

** of an inch in length. This, which is in itself a

" particular line, is nevertheless, with regard to its

*' signification, general, since, as it is there used, it

** represents all particular lines whatsoever, so that

*' what is demonstrated of it, is demonstrated of all

*' lines, or, in other words, of a line in generaL And** as that particular line becomes general by being

** made a sign, so the name lirie, which, taken abso-

*' lutely, is particular, by being a sign, is made•* general.

" Here,'* continues Dr Reid, " I observe, that

" when a particular idea is made a sign to represent

" and stand for all ofa soj^l, this supposes a distinc-

" tion of things into sorts or species. To be of a sort^

*' implies having those attributes which characterize

" the sort, and are common to all the individuals

" that belong to it. There cannot, therefore, be a

" sort without general attributes ; nor can there be

" any conception of a sort without a conception of

** those general attributes which distinguish it. The


" conception of a sort, therefore, is an abstract

" general conception.

** The particular idea cannot surely be made a

" sign of a thing of which we have no conception.

" I do not say, that you must have an idea of the

" sort ; but surely you ought to understand or

** conceive what it means, when you make a particu-

" lar idea a representative of it ; otherwise your

*' particular idea represents you know not what."*

Although I do not consider myself as called up-

on to defend all the expressions which Berkeley may

have employed in support of his opinion on this ques-

tion, I must take the liberty of remarking, that, in

the present instance, he appears to me to have been

treated with an undue severity. By ideas of the

same sort, it is plain he meant nothing more than

things called by the same name, and, consequently

(if our illustrations are to be borrowed from mathe-

matics), comprehended under the terms of the same

definition. In such cases, the individuals thus

classed together are completely identifeddi^ subjects

of reasoning j insomuch, that what is proved with

respect to one individual, must hold equally true of

all the others. As it is an axiom in geometiy, that

things which are equal to one and the same thing,

are equal to one another ; so it may be stated as a

maxim in logic, that whatever things have the same

name applied to them, in consequence of their being

comprehended in the terms of the same definition,

may all be considered as the same idcntic<d siilfject,

* Pages 484, 485.


in every case where that definition is the principle

on which our reasoning proceeds. In reasoning,

accordingly, concerning any sort or species of things,

our thoughts have no occasion to wander from the

individual sign or rejjresentative to which the at-

tention happens to be directed, or to attempt the

fruitless task of grasping at those specific varieties

which are avowedly excluded from the number of

our premises. As every conclusion which is logical-

ly deduced from the definition must, of necessity,

hold equally true of all the individuals to which the

common name is applicable, these individuals are re-

garded merely as so many units, which go to the

composition of the multitude comprehended under

the collective or generic term. Nor has the power

of conception anything more to do in the business,

than when we think of the units expressed by a par-

ticular number in an arithmetical computation.

The word sor^t is evidently transferred to our in-

tellectual arrangements, from those distributions of

material objects into separate heaps or collections,

which the common sense of mankind universally

leads them to make for the sake of the memory ; or

(which is perhaps nearly the same thing) with a view

to the pleasure arising from the perception of order.

A familiar instance of this presents itself in the

shelves, and drawers, and parcels, to which every

sho])keeper has recourse for assorting, according to

their respective denominations and prices, the va-

rious articles which compose his stock of goods. In.

one parcel (for example) he collects and incloses un-

der one common envelope, all his gloves of a parti-

12!^ ELEMENTS OF THE PHILOSOPHY Chap. II.

cukr size and quality ; in another, all his glo'ves of

a different size and quality ; and, in like manner, he

proceeds with the stockings, shoes, hats, and the va-

rious other commodities with which his warehouse

is filled. By this means, the attention of his shop-

boy, instead of being bewildered among an infinitude

of particulars, is confined to parcels or assortments

of particulars ; of each of which parcels a distinct

idea may be obtained from an examination of any one

of the individuals contained in it. These indivi-

duals, therefore, are, in his apprehension, nothing

more than so many units in a multitude, any one or

which units is perfectly equivalent to any other

;

while, at the same time, the parcels themselves, not-

withstanding the multitude of units of which they

are made up, distract his attention, and burden his

memory as little as if they were individual articles.

The truth is, that they become to his mind indivi-

dual objects of thought^ like a box of counters, or a

rouleau of guineas, or any of the other material ag-

gregates with which his senses are conversant ; or,

to take an example still more apposite to our present

purpose, like the phrases one thousand, or one mil-

lion, when considered merely as simple units enter-

ing into the composition of a numerical sum.

The task which I have here supposed the trades-

man to perform, in order to facilitate the work of his

shop-boy, is exactly analogous, in its effect, to the

aid which is furnished to the infimt understanding

by the structure of its mother-tongue ; the generic

words which abound iu language assorting and (if I

may use the expression) packing up^ under a compa-it'

Sect. 1?. OJ THE HUHJAN MIND. 1^ratively small number of comprehensive terms, the

multifarious objects of human knowledge.* In con-

sequence of the generic terms to which, in civilized

society, the mind is early familiarized, the vast mul-

tiplicity of things which compose the furniture of

this globe are presented to it, 7wt as they occur to

the senses of the untaught savage, but as they have

been arranged and distributed into parcels or assort-

ments by the successive observations and reflections

of our predecessors. Were these arrangements and

distributions agreeable, in every instance, to sound

philosophy, the chief source of the errors to which

we are liable in all our general conclusions would

be removed ; but it would be too much to expect

(with some late theorists) that, even in the most ad-

vanced state either of physical or of moral science,

this supposition is ever to be realized in all its ex-

tent. At the same time, it must be remembered,

that the obvious tendency of the progressive reason

and experience of the species, is to diminish, more

and more, the imperfections of the classifications

which have been transmitted from ages of compa-

rative ignorance ; and, of consequence, to render

language, more and more, a safe and powerful organ

lor the investigation of truth.

The only science which furnishes an exception to

these observations is mathematics ; a science essen-

tially distinguished from every other by this remark-

* The same analogy had occurred to Locke. " To shorten

** its way to knowledge, and make each perception more com-'* prehensive, the mind binds them into bundles."

VOL. II. I

^


able circumstance, that the precise import of its ge-

neric terms is fixed and ascertained by the definitions

which form the basis of all our reasonings, and in

which, of consequence, the very possibility of error

in our classifications is precluded, by the virtual iden-

tity of all those hypothetical objects of thought to

which the same generic tenn is applied.

I intend to prosecute this subject farther, before

concluding my observations on general reasoning.

At present, I have only to add to the foregoing re-

marks, that, in the comprehensive theorems of the

philosopher, as well as in the assortments of the

tradesman, I cannot perceive a single step of the

understanding, which implies anything more than

the notion of number, and the use of a commonname.

Upon the whole, it appears to me, that the cele-

brated dispute concerning abstract general ideas,

"which so long divided the schools, is now reduced,

among correct thinkers, to this simple question of

fact. Could the human mind, without tJie use ofsigns

of one hind or another, have carried on general

reasonings, or formed general conclusions ? Before

arguing with any person on the subject, I should

wish for a categorical explanation on this prelimina-

ry point. Indeed, every other controversy con-

nected with it turns on little more than the meaning

of words.

A difference of opinion with respect to this ques-

tion oijact (or rather, I suspect, a want of attention

in some of the disputants to the great variety of signs

of which the mind can avail itself, independently of

StcU C. OF THE HUMAN MIND. 131

words) still continues to keep up a sort of distinction

between the Nominalists and the Conceptualists.

As for the Realists, they may, I apprehend, be fairly

considered, in the present state of science, as having

been already forced to lay down their arms.

That the doctrine of the Nominalists has been

stated by some writers of note in very unguarded

terms, I do not deny, * nor am I certain that it was

* Particularly by Hobbes, some of whose incidental remarks

and expressions would certainly, if followed strictly out to their

logical consequences, lead to the complete subversion of truth, as

a thing real, and independent of human opinion. ? It is to this,

I presume, that Leibnitz alludes, when he says of him, " Thomas

" Hohbes, qui ut verumfatear, mihi plus quam nommalis videtur.'

I shall afterwards point out the mistake by which Hobbes

seems to me to have been misled. In the meantime, it is but

justice to him to say, that I do not think he had any intention to

establish those sceptical conclusions which, it must be owned,

may be fairly deduced as corollaries from some of his principles.

Of this I would not wish for a stronger proof than his favourite

maxim, that " words are the counters of wise men, but the money

" of fools ;" a sentence which expresses, with marvellous concise-

ness, not only the proper function of language, as an instrument

of reasoning, but the abuses to which it is liable, when in unskil-

ful hands.

Dr Gillies, who has taken much pains to establish Aristotle's

claims to all that is valuable in the doctrine of the Nominalists,

has, at the same time, represented him as the only favourer of

this opinion, by whom it has been taught without any admixture

of those errors which are blended with it in the works of its mo-

dern revivers. Even Bishop Berkeley himself is involved with

Hobbes and Hume in the same sweeping sentence of condemna-

tion. " The language of the Nominalists seems to have been ex-

** tremely liable to be perverted to the purposes of scepticism,

*' as taking away the specific distinctions of things ; and is in

*' fact thus perverted by Hobbes, Berkeley, Hume, and their in-

132 ELEMENTS OF THE PHILOgOPHT Chap. II.

ever delivered by any one of the schoolmen in a

form completely unexceptionable ; but after the lu-

minous, and, at the same time, cautious manner in

which it has been unfolded by Berkeley and his suc-

cessors, I own it appears to me not a little surprising,

that men of talents and candour should still be found

inclined to shut their eyes against the light, and to

shelter themselves in the darkness of the middle

ages. For my own part, the longer and the more

attentively that I reflect on the subject, the more amI disposed to acquiesce in the eulogium bestowed on

Roscellinus and his followers by Leibnitz ; one of

the very few philosophers, if not the only philoso-

pher of great celebrity, who seems to have been fully

aware of the singular merits of those by whom this

theory was originally proposed : " secta nomina-" LIUM, OMNIUM INTER SCHOLASTICAS PROFUNDIS-" SIMA, ET HODIERN.E REFORMATiE PHILOSOPHAN-" Di RATiONi coNGRUENTissiMA.'* It is a theory, in-

deed, much more congenial to the spirit of the eight-

eenth than of the eleventh century ; nor must it be

forgotten, that it was proposed and maintained at a

period when the algebraical art (or, to express my-

" numerablefollowers . But Aristotle's language is not liable to

*' this abuse."

—

Giliics's Aristotle, Vol. I. p. 71, 2d edit.

Among these sccpticul followers of Berkeley, we must, I pre.

fume, include the late learned and ingeriious Dr Campbell;

whose remarks on this subject I will, nevertheless, venture to re-

commend to the particular attention of my readers. Indeed, I

tlo not know of any writer who has treated it with more acute-

ness and perspicuity.—Sec Philosophy of Rhetoric, Book II.

(liap, vii.

Sect. 2. OF THE HUMAN MIND. IS-^

self more precisely, universal arithmetic), from which

we now borrow our best illustrations in explaining

and defending it, was entirely unknown.

II.

Continuation of the Subject.—Of Language consi-

dered as an Instrument of Thought.

Having been led, in defence of some of my own

opinions, to introduce a few additional remarks on

the controversy with respect to the theory oi general

reasonings I shall avail myself of this opportunity to

illustrate a little farther another topic (intimately

connected with the foregoing argument), on which

the current doctrines of modern logicians seem to

require a good deal more of explanation and restric-

tion than has been commonly apprehended. Upon

this subject I enter the more willingly, that, in myfirst volume, I have alluded to these doctrines in a

manner which may convey, to some of my readers,

the idea of a more complete acquiescence, on mij

part, in their truth, than I am tlisposed to acknow-

ledge.

In treating of abstraction, I endeavoured to shew

that we tliink, as well as speak, by means of words,

and that, without the use of language, our reasoning

faculty (if it could have been at all exercised) must

necessarily have been limited to particular conclu-

sions alone. The effects, therefore, of ambiguous

and indefinite terms are not confined to our com- \

munications with others, but extend to our private \and solitary speculations. Dr Campbell, in his Plri- /

/


losophy of Rhetoric, has made some judicious and

important observations on this subject ; and, at a

much earlier period, it drew the attention of Des-

cartes ; who, in the course of a very valuable discus-

sion with respect to the sources of our errors, has

laid particular stress on those to which we are expos^

ed from the employment of language as an instru-

ment of thought. " And, lastly, in consequence of

*' the habitual use of speech, all our ideas become

" associated with the words in which we express

*' them ; nor do we ever commit these ideas to me-

" moiy, without their accustomed signs. Hence it

" is, that there is hardly any one subject, of which

'* we have so distinct a notion as to be able to think

" of it abstracted from all use of language ; and, in-

*' deed, as we remember words more easily than

*' things, our thoughts are much more conversant

*' with the former than with the latter. Hence, too,

** it is, that we often yield our assent to propositions,

" the meaning ofwhich we do not understand; ima-

" gining that we have either examined formerly

*' the import of all the terms involved in them, or

*' that we have adopted these terms on the authori-

" ty of others upon whose judgment we can rely."*

* " Et denique, propter loquelae usum. conceptos omnes nos-

*' tros verbis, quibus cos exprimiinus, alliaamus, nee eos, nisi si-

" mul cum istis verbis, memorise mandamus. Cumque facilius

" postea verborum quara rerum recordemur, vix unquam uUius

" rei conceptum habemus tarn distinctum, ut ilium ab omni ver-

" borum conceptu separemus ; cogitationesque hominum fere

"•' omnium, circa verba magis quam circa res versantur ; adeo ut

*' persaepe vocibus non intellcctis prasbeant asscnsum, quia pu-

I


To these important considerations, it may be

worth while to add, that whatever improvements

*' tant se illos olim intellexisse, vel ab aliis qui eas recte intcUigc-

*' bant, accepisse."

—

Princ. Pfiil. Pars Prima, Ixxiv.

I have quoted a very curious passage, nearly to the same pur-

pose, from Leibnitz, in a note annexed to my first volume (see

Note L.) I was not then aware of the previous attention which

bad been given to this source of error by Descartes; nor did I

expect to find so explicit an allusion to it in the writings of Ari-

stotle, as I have since observed in the following paragraph :

A/0 xai rm Taâ rr^v Xs^/v buTog 6 rÔ'rrog dsnog' 'Xûrov fLiv, or/

fidKXov y} a~ar-fj yinrai îit aXKm ffx.o'Xov/Mivoii n %aS itcvroug' tj /X:v

yap fhir aXkm ff'/.i-îg dia >,oys" 55 8i /caff durovg, a^ r,rlov di aura

Tn rrâyfjitarog' ura, xai -/.aff dvroug arraraffdai gu/JblSaivsi, hrav sot ns

"kayts ToiTirai rr/v cks-îv er/, ri fiiv arrarri £X rjjs o/M6iorrirog' tj 6s o/m-

lorrig, sx rrig Xiîug.—De Sophist. Elenckis, Lib. I. cap. vii.

" Quocirca inter eos (Paralogismos) qui indictione consislunt,

*' hie fallendi modus est ponendus. Primum, quia magis decipi-

*' mur considerantes cum aliis, quam apud nosmetipsos : nam'* consideratio cum aliis per sermonem instituitur;apud nosmet-

'* ipsos autem non minus fit per rem ipsam. Deinde et per

*' nosmetipsos ut fallamur accidit, cum in rebus considerandis

*' sermo adhibetur: Pra?terea deceptio est ex similitudine : si-

" militudo autem ex dictione."—Edit. Du Vat. Vol. I. p. 239.

Lest it should be concluded, however, from this detached re-

mark, that Aristotle had completely anticipated Locke and Con-

dillac in their speculations with respect to language, considered

as an instrument of thought, I must beg of my readers to compare

it with the previous enumeration given by the same author, of

those paralogisms or fallacies which Y\q in the diction (De Sophist.

JE,lenchis, Lib. i. cap. 4.) ;—recommending to them, at the same

time, as a useful comment on the original, the twentieth chapter

of the third book of a work entitled Institutio Logica, by the

learned and justly celebrated Dr Wallis of Oxford. I select this

work in preference to any other modern one on the same subject,

AS it has been lately pronounced, by an authority for which I en-

tertain a sincere respect, to be " a complete and accurate trea-


may yet be iiiatle in language by philosophers, they

never can relieve the student from the indispensa-

ble task of analyzing, with accuracy, the complex

ideas he annexes to the terms employed in his rea-

sonings. The use of general terms, as Locke has

remarked, is learned, in many cases, before it is pos-

sible for us to comprehend their meaning ; and the

greater part ofmankind continue to use them through

life, without ever being at the trouble to examine

accurately the notions they convey. This is a study

which every individual must carry on for himself;

and of which no rules of logic (how useful soever

they may be in directing our labours) can supersede

the necessity.

Of the essential utility of a cautious employment

of words, both as a medium of communication and

as an instrument of thought, many striking illustra-

tions might be produced from the history of science

during the time that the scholastic jargon was cur-

rent among the learned ; a technical phraseology,

which was not only ill calculated for the discovery of

truth, but which was dexterously contrived for the

" tise of logic, strictly according to the Aristotelian method :"

and as wo are farther told that it is ' still used by many in the

" university to which Wallis belonged, as the lecture-book iu that

" department of study." I intend to quote part of this chapter

on another occasion. At present, I shall only observe, that it

does not contain the slightest reference to the passage which has

led me to introduce these observations ; and which, I believe,

will be now very generally allowed to be of greater value than all

those puerile distinctions put together, which Dr Wallis has been

at so much pains to illustrate and to exemplify.

5

Sect. 2. <>F THE HU3IAN 3fIND. 137

propagation of error ; and whicli gave to those who

were habituated to the use of it, great advantages in

controversy (at least in the judgment of tlie multi-

tude) over their more enlightened and candid oppo-

nents. *' A blind wrestler, by fighting in a dark

•* chamber,*' to adopt an allusion of Descartes,

" may not only conceal his defect, but may enjoy

*' some advantages over those who see. It is the

" light of day only that can discover his inferiority."

The imperfections of this philosophy, accordingly,

have been exposed by Descartes and his followers,

less by the force of their reasonings, than by their

teaching men to make use of their own faculties, in-

stead of groping in the artificial darkness of the

schools ; and to perceive the folly of expecthig to

advance science by ringing changes on words to

which they annexed no clear or precise ideas.

In consequence of the influence of these views,

the attention of our soundest philosophers was more

and more turned, during the course of the last cen-

tuiy, to the cultivation of that branch of Logic

which relates to the use of words. Mr Locke's ob-

servations on this subject form, perhaps, the most

valuable part of his writings ; and, since his time,

much additional light has been thrown upon it by

Condillac and his successors.

Important, however, as this branch of logic is in

its practical applications, and highly interesting,

from its intimate connection with the theory of the

human mind, there is a possibility of pushing, to an

erroneous and dangerous extreme, the conclusions to

which it has led. Condillac himself falls, in no in-

138 ELEMENTS OP THE PHILOSOPHY Chap. 11.

considerable a degree, under this censure ; having,

upon more than one occasion, expressed himself as

if he conceived it to be possible, by means of precise

and definite terms, to reduce reasoning, in all the

sciences, to a sort of mechanical operation, analogous,

in its nature, to those which are practised by the al-

gebraist, on letters of the alphabet. " The art of

" reasoning," he repeats over and over, *' is nothing

*' more than a language well arranged."—" L'art

*' de raisonner se reduit a une langue bein faite."

One of the first persons, as far as I know, who

objected to the vagueness and incorrectness of tliis

proposition, was M. De Gerando ; to whom we are

farther indebted for a clear and satisfactory exposi-

tion of the very important fact to which it relates.

To this fact Condillac approximates nearly in va-

rious parts of his works ; but never, perhaps, without

some degree of indistinctness and of exaggeration.

The point of view in which it is placed by his inge-

nious successor, strikes me as so just and happy, that

I cannot deny myself the pleasure of enriching my

book with a few of his observations,

" It is the distinguishing characteristic of a lively

*' and vigorous conception, to push its speculative

" conclusions somewhat beyond their just limits.

*' Hence, in the logical discussions of this estimable

" writer, these maxims (stated without any explana-

*' tion or restriction), * That the study of a science

*' is nothing more than the acquisition of a lan-

" (Xuage ;' and, * that a science properly treated is

*' o?iIi/ a language well contrived.* Hence, the

" rash assertion, * That mathematics possess no ad'

11

SfecL 2. OP THE HUMAN MIND. 139

" vantage over other sciences, hut 'what they derive

*^from a better phraseology ; and that all of these

" might attain to the same characters of simplicity

** and of certainty, if we knew hoxc to give them

** signs equally perfect.' '' *

" The same task which must have been executed

" by those who contributed to the first formation of

" a language, and which is executed by every child

" when he learns to speak it, is repeated over in the

" mind of every adult when he makes use of his mo-

" ther-tongue ; for it is only by the decomposition

" of his thoughts that he can learn to select the

*' signs which he ought to employ, and to dispose

" them in a suitable order. Accordingly, those ex-

** ternal actions which we call spealing or xvrifingy

" are always accompanied with a philosophical pro-

*' cess of the understanding, unless we content our-

** selves, as too often happens, with repeating over

" mechanically what has been said by others. It is

" in this respect that languages, with their forms

" and rules, conducting (so to speak) those who" use them into the path of a regular analysis

;

" tracing out to them, in a well ordered discourse,

" the model of a perfect decomposition, may be re-

** garded, in a certain sense, as analytical methods," But I stop short ; Condillac, to whom this

" idea belongs, has developed it too well to leave

^' any hope of improving upon his statement."

In a note upon this passage, however, M. De Ge-

rando has certainly improved not a little on the

* Des Signcs et de I'Art de Pciiser, kc, Introd. pp. xx. xxi.

140 ELEMENTS OF THE PHILOSOPHY Chap. If.

statement of Condillac. " In asserting,'* says he,

" that languages may be regarded as analytical me-*' thods, I have added the qualifying phrase, in a

*' certain sense, for the word method cannot be em-

" ployed here with exact propriety. Languages*' furnish the occasions and the means ofanalysis ;

" that is to say, they afford us assistance m.following

*' that method ; but they are not the method itself.

" They resemble signals or finger-posts placed on a

" road to enable us to discover our way ; and if they

*' help us to analyze, it is because they are them-

" selves the results, and, as it were, the monuments*' of an analysis which has been previously made

;

" nor do they contribute to keep us in the right

" path, but in proportion to the degree ofjudgment

" with which that analysis has been conducted." *

I was the more solicitous to introduce these ex-

cellent remarks, as I suspect that I have myself in-

directly contributed to propagate in this country the

erroneous opinion which it is their object to correct.

By some of our later writers it has not only been

implicitly adopted, but has been regarded as a con-

clusion of too great value to be suffered to remain

in the quiet possession of the moderns. " Aristotle/*

says the author of a very valuable analysis of his

works, " xoell knew that our knowledge of things

" chiefly depending on the proper application of lan-

" guage as an instrument of thought, the true art

" of reasoning is nothing but a language accurately

** defined and skilfully arranged ; an opinion which,

* Des Sigues et de I'Art di- Pcnser, &c. pp. 138, 159, Tom. I.


** after many idle declamations against his barren

" generalities and verbal trifling, philosophers have

" begun very generally to adopt.'* *

Aristotle's Ethics, &c. by Dr Gillies, Vol. I. p. 94, 2d edit.

The passage in my first volume, to which I suspect an allusion

is here made, is as follows

:

" The technical terms, in the different sciences, render the ap-

" propriate language of philosophy a still more convenient instru-

" MEKT OF THOUGHT, than those languages which have originat-

" ed from popular use ; and in proportion as these technical

" terms improve in point of precision and of comprehensive-

** ness, they will ccmtribute to render our intellectual progress

" more certain and more rapid. ' While engaged,' says Mr La-

" voisier, * in the composition of my Elements of Chemistry, I

" perceived, better than 1 had ever done before, the truth of an

" observation of Condillac, that we think only through the me-

" dium of words, and that languages are true analytic methods.

" Algebra, which, of all our modes of expression, is the most

** simple, the most exact, and the best adapted to its purpose, is,

" at the same time, a language and an analytical method. The*' art of reasoning is nothing rnore than a language well arranged.'

'* The influence," I have added, " which these very enlightened and

" philosophical views have already had on the doctrines of che-

" mistry, cannot fail to be known to most of my readers."

When this paragraph was first written, I was fully aware of

the looseness and indistinctness of Lavoisier's expressions ; but as

my only object in introducing the <juotation was to illustrate the

influence of general logical princij)les on the progress of particu-

lar sciences, I did not think it necessary, in the introduction to

ray work, to point out in what manner Condillac's propositions

were to be limited and corrected. I am truly happy, for the sake

of M. De Gerando, that I happened to transcribe them in the

same vague and very exceptionable terms in which I found them

sanctioned by the names of Condillac, and of one of the most illus-

trious of his disciples.

It will not, I hope, be considered as altogether foreign to the


After this strong and explicit assertion of th6

priority of Aristotle's claim to the opinion which

we are here told *' philosophers begin very gene-

" rally to adoptf^' it is to be hoped, that M. DeGerando will be in future allowed to enjoy the un-

disputed honour of having seen a little farther into

this fundamental article of logic than the Stagirite

himself.

III.

Continuation oj^ the Subject.— Plsionary Theories

ofsome Logicians^ occasioned by their inattention

to the Essential Distinction between Mathematics

and other Sciences.

In a passage already quoted frotn De Gerando,

he takes notice of what he justly calls a rash asser-

tion of Cojidillac^ " That mathematics possess no

" advantage over other sciences, but what they de-

** rive from a better phraseology ; and that all of

*' them might attain to the same characters of sim-

dcsign of this note, if I remark further, how easy it is for a trans-

lator of Aristotle (in consequence of the unparalleled brevity

which he sometimes affects) lo accommodate the sense of the ori-

ginal, by the help of paraphrastical clauses, expressed in the

phraseology of modern science, to every progressive step in the

history of human knowledge. In truth, there is not one philoso-

pher of antiquity, whose opinions, when they are stated in any

terms but his own, are to be received with so great distrust.

The unsoundness of Condillac's assertion, that the art of rea-

soning is nothing more than a language "well arranged, was, I be-

lieve, first pointed out by M. Prevost—Sec some acute and de-

cisive objections to this proposition in his Treatise J)es Sign^s,

kc. Paris, An. VIII. p. 20.

Sect. 2. OB" THE HUMAN MlifD. 113

** plicity and of certainty, if we knew how to give

*' them sig?is equally perfect.'*

Leibnitz seems to pohit at an idea of the same

sort, in those obscure and enigmatical hints (not

altogether worthy, in my opinion, of his powerful

and comprehensive genius) which he has repeatedly

thrown out, about the miracles to be effected by a

new art of his own invention ; to which art he some-

times gives the name of Ars Combinatoria Ckarac-

teristica, and sometimes of Ai^s Combinatoria Gene-

ralis ac Vera. In one of his letters to Mr Olden-

burg he speaks of a plan he had long been meditat-

ing, of treating of the science of Mind by means of

mathematical demonstrations. " Many wonderful

" things,'* he adds, " of this kind have occurred to

" me, which, at some future period, I shall explain to

* the public with that logical precision which the

*' subject requires.** * In the same letter, he inti-

mates his belief in the possibility of inventing an

art, " which, with an exactitude resembling that of

*' mechanism, may render the operations of reason

" steady and visible, and, in their effects on the

" minds of others, irresistible.** t After which he

proceeds thus :

*' Our common algebra, which we justly value so

" highly, is no more than a branch of that general

*' art which I have here in view. But, such as it is,

" it puts it out of our power to commit an error,

* " MuUa ill hoc geneie mira a me sunt observata, quae

" aliquando, quo par est rigore, exposita dabu."

t *' Quod velut mechanica ralione fixam et visibilcm et (ut

" itra dicani^ irresistibilera reddat rationora.''


" even altliougli we should wish to do so ; while it

*' exhibits truth to our eyes like a picture stamped*' on paper by means of a machine. It must, at the

" same time, be recollected, that algebra is indebted

'* for whatever it accomplishes in the demonstration

*' of ^''^^2<?r^// theorems to the suggestions of a higher

" science ; a science which I have been accustomed

"to cdW characteristical combination ; very differ-

*' ent, however, in its nature, from that which these

*' words are likely, at first, to suggest to the hearer.

*' The marvellous utility of this art I hope to illus-

•' trate, both by precepts and examples, if I shall be*' so fortunate as to enjoy health and leisure.

*' It is impossible for me to convey an adequate

" idea of it in a short description. But this I may" venture to assert, that no instrument (or organ)

*' could easily be imagined of more powerful effi-

" cacy for promoting the improvement of the human" understanding ; and that, supposing it to be adopt-

*' ed as the common method of philosophizing, the

*' time would very soon arrive, when we should be** able to fonn conclusions concerning God and the

*' JNIind, with not less certainty than we do at pre-

" sent concerning figures and numbei's." *

The following passage is translated from another

letter of Leibnitz to the same correspondent

:

** The matter in question depends on another of

" much higher moment ; I mean, on a general and'* true art ofcombination, of the extensive influence

*' of which I do not know that any person has yet

* Wallisii Opera, Vol. III. p. 621.


" been fully aware. This, in tmtli, does not differ

" from that sublime analysis, into the recesses of

" which Descartes himself, as far as I can judge,

** was not able to penetrate. But, in order to cany

" it into execution, an alphabet of human thoughts

*' must be previously formed ; and tor the invention

*' of this alphabet, an analysis of axioms is indispen-

" sably necessary. I am not, however, surprised,

*' that nobody has yet sufficiently considered it

;

" for we are, in general, apt to neglect what is easy ;

*' and to take many things for granted, from their

*' apparent evidence ; faults which, while they re-

" main uncorrected, will for ever prevent us from

" reaching the summit of things intellectual, by the

*' aid of a calculus adapted to moral as well as to

" mathematical science.*' *

In these extracts from Leibnitz, as well as in that

quoted from Condillac, in the beginning of this

article, the essential distinction between mathema-

tics and the other sciences, in point of phraseology,

is entirely overlooked. In the former science,

where the use of an ambiguous word is impossible,

* Wallisii Opera, Vol. III. p. 633.

As these reveries of this truly great man are closely connected

with the subsequent history of logical speculation in more than

one country of Europe, I have been induced to incorporate them

in an English version, with my own disquisitions. Some ex-

pressions, which, I am sensible, are not altogether agreeable to

the idiom of our language, might have been easily avoided, if I

had not felt it incumbent on me, in translating an author whose

meaning, in jthis instance, I was able but very imperfectly to

comprehend, to deviate as little as possible from his own words.

VOL. II. K


it may be easily conceived how the solution of a pro-

blem may be reduced to something resembling the

operation of a mill,—the conditions of the problem,

when once translated from the common language

into that of algebra, disappearing entirely from the

view; and the subsequent process being almost

mechanically regulated by general rules, till the final

result is obtained. In the latter, the whole of the

words about which our reasonings are conversant,

admit, more or less, of different shades of meaning ;

and it is only by considering attentively the relation

in which they stand to the immediate context, that

the precise idea of the author in any particular in-

stance is to be ascertained. In these sciences, ac-

cordingly, the constant and unremitting exercise of

the attention is indispensably necessary, to prevent

us, at every step of our progress, from going astray.

On this subject I have made various remarks in a

volume lately published ; to which I beg leave here

to refer, in order to save the trouble of unnecessaiy

repetitions. * From w^hat I have there said, I trust

it appears that, in following any train of reasoning,

beyond the circle of the mathematical sciences, the

mind must necessarily carry on, along with the logi-

cal deduction expressed in words, another logical

process of a far nicer and more difficult nature ;

—

that of fixing, with a rapidity which escapes our me-

mory, the precise sense of every word which is am-

biguous, by the relation in which it stands to the

2 general scope of the argument. In proportion as

* Philosophical Essays, p. 153, et se^. 4t,o edit.

Sect. 2. OF THE HUMAN MIND. 14<7

the language of science becomes more and more

exact, the difficulty of this task will be gradually

diminished ; but let the improvement be carried to

{iny conceivable extent, not one step will have been

gained in accelerating that aera, so sanguinely antici-

pated by Leibnitz and Condillac, when our reason-

ings in morals and politics shall resemble, in their

mechanical regularity, and in their demonstrative

certainty, the investigations of algebra. The im-

provements w hich language receives, in consequence

of the progress of know^ledge, consisting rather in

a more precise distinction and classification of the va-

rious meanings of words, than in a reduction of these

meanings in point of number, the task of mental

induction and interpretation may be rendered more

easy and unerring ; but the necessity of this task

can never be superseded, till every word which we

employ shall be as fixed and invariable in its signi-

fication as an algebraical character, or as the name

of a geometrical figure.

In the meantime, the intellectual superiority of

one man above another, in all the different branches

of moral and political philosophy, will be found to

depend chiefly on the success with which he has

cultivated these silent habits ofinductive interjireta-

tion,—much more, in my opinion, than on his ac-

quaintance with those rules which form the great

objects of study to the professed logician. In proof

of this, it is sufficient for me to remind my readers,

that the whole theory of syllogism proceeds on the

supposition that the same word is always to be em-

ployed precisely in the same sense (for otherwise

148 ELEMENTS OF THE PHILOSOPHY Chap, II.

the syllogism would be vitiated by consisting of morethan three terms), and, consequently, it takes for

granted, in every rule which it furnishes for the

guidance of our reasoning powers, that the nicest,

and by far the most difficult part of the logical pro-

cess, has been previously brought to a successful ter-

mination.

In treating of a different question, I have else-

where remarked, that although many authors have

spoken of the wonderful mechanism ofs'peech^ none

has hitherto attended to the far more wonderful

mechanism which it puts into action behind the

scene. A similar observation will be found to apply

to what is commonly called the Art of Reasoning.

The scholastic precepts which profess to teach it

reach no deeper than the very surface of the sub-

ject ; being all of them confined to that part of the

intellectual process which is embodied in the form

of verbal propositions. On the most favourable

supposition v;hich can be formed with respect to

them, they are superfluous and nugatory ; but, in

many cases, it is to be apprehended, that they inter-

fere with the right conduct of the understanding, by

withdrawing the attention from the cultivation of

that mental logic on which the soundness of our

conclusions essentially depends, and in the study of

which (although some general rules may be of use)

every man must be, in a great measure, his own

master.*

* Those who are intcrcsled in this discussion, will enter more

completely into my views, if they take the trouble to combine

what is hire stated, with some observations I have introduced in

the first volume of this work. See p. 177, ct seq, 3d edit.

Sect. 'J.OF THE HUMAN MIND. 14*9

In the practical application of tlie foregoing con-

clusions, it cannot fail to occur, as a consideration

equally obvious and important, that, in proportion as

the objects of our reasoning are removed from the

particular details with which our senses are conver-

sant, the difficulty of these latent inductive pro-

cesses must be increased. This is the real source

of that incapacity for general speculation, which MrHume has so well described as a distinguishing

characteristic of uncultivated minds. *' General rea-

" sonings seem intricate, merely because they are

" general ; nor is it easy for the bulk of mankind to

** distinguish, in a great number of particulars, that

" common circumstance in which they all agree,

*' or to extract it, pure and unmixed, from the other

*' superfluous circumstances. Every judgment or

*' conclusion with them is particular. They cannot

*' enlarge their views to those universal propositions

*' which comprehend under them an infinite number*' of individuals, and include a whole science in

*' a single theorem. Their eye is confounded with

*' such an extensive prospect, and the conclusions

*' deduced from it, even though clearly expressed,

*' seem intricate and obscure." *

Difficult, however, and even impossible as the task

of general speculation is to the bulk of mankind, it

is nevertheless true, that it is the path which leads

the cautious and skilful reasoner to all his most cer-

tain, as well as most valuable, conclusions in morals

and politics. If a theorist, indeed, should expect that

these conclusions are, in every particular instance,

* Essay on Commerce.

r


to be realized, he would totally misapprehend their

nature and application ; inasmuch as they are only

to be brought to an experimental test, by viewing

them on an extensive scale, and continuing our ob-

servations during a long period of time. " When" a man deliberates," says Mr Hume, *' concerning

" his conduct in any 'particular affair, and forms

"schemes in politics, trade, economy, or any business

" in life, he never ought to draw his arguments too

" fine, or connect too long a chain of consequences

" together. Something is sure to happen that will

*' disconcert his reasoning, and produce an event dif-

" ferent from what he expected. But when we" reason upon general subjects, one may justly

*' affirm, that our speculations can scarcely ever be

" too fine, provided they be just ; and that the dif-

" ference between a common man and a man of

" genius is chiefly seen in the shallowness or depth

" of the principles on which they proceed." The

same author afterwards excellently observes, *' That*' general principles, however intricate they may" seem, must always prevail if they be just and*' sound, in the general course of things, though they

*' may fail in particular cases ; and that it is the

" chief business of philosophers to regard the gene-

" ral course of things."—" I may add," continues

Mr Hume, *' that it is also the chief business of

*' politicians, especially in the domestic government

" of the state, where the public good, which is, or

" ought to be, their object, depends on the concur-

'* rence of a multitude of causes ; not, as in foreign

12


" politics, on accidents and chances, and the caprices

** of a few persons." *

To these profound reflections of Mr Hume, it

may be added (although the remark does not bear

directly on our present argument), that, in the syste-

matical application of general and refined rules to

their private concerns, men frequently err from calcu-

lating their measures upon a scale disproportionate

to the ordinary duration of human life. This is one

of the many mistakes into which projectors are apt

to fall ; and hence the ruin which so often over-

takes them, while sowing the seeds of a harvest

which others are to reap. A few years more might

have secured to themselves the prize which they had

in view ; and changed the opinion of the world

(which is always regulated by the accidental circum-

stances of failure or of success) from contempt of

their folly, into admiration of their sagacity and per-

severance.

It is observed by the Comte de Bussi, that " time

" remedies all mischances ; and that men die un-

" fortunate, only because they did not live long

* Essay on Commerce.

This contrast between the domestic and the foreign policy of a

stale occurs more than once in Mr Hume's writings. (See in par-

ticular the first paragraphs of his Essay on the Rise of Arts and

Sciences). A similar observation had long before been made by

Polybius. " There are two ways by which every kind of go-

" vernment is destroyed : either by some accident that happens

" from without, or some evil that arises within itself; When*' the first will be, it is not always easy to foresee ; but the latter

' iscertain and determinate,"—Book VI. Ex- 3, (Hampton's Trans-

lation.)

16^ ELEMENTS OF THE PHILOSOPHY Chap. II.

" enough. Mareschal d'Estree, who died rich at a

** hundred, would have died a beggar, had he lived

" only to eighty.*' The maxim, like most other

apothegms, is stated in terms much too unqualified

;

but it may furnish matter for many interesting re-

flections to those who have surveyed with attention

the characters which have passed before them on

the stage of life ; or who amuse themselves with

marking the trifling and fortuitous circumstances

by which the multitude are decided, in pronoimcing

their verdicts of foresight or of improvidence.

IV.

Continuation of the Subject.—Peculiar- and superemi-

726nl Advantages possessed hy Matliematicians,

in consequence of their definite Phraseology,

If the remarks contained in the foregoing articles

of ,this section be just, it will follow, that the various

artificial aids to our reasoning powers which have

been projected by Leibnitz and others, proceed on

the supposition (a supposition which is also tacitly

assumed in the syllogistic theory) that, in all the

sciences, the words which we employ have, in the

course of our pretious studies, been brought to a

sense as unequivocal as the phraseology of mathema-

ticians. They proceed on the supposition, there-

fore, that by far the most difficult part of the logical

problem has been already solved. Should the period

ever arrive, when the language of moralists and po-

liticians shall be rendered as perfect as that of geo-

meters and algebraists, the?i, indeed, may such con-

S«et. 2. 01? THE HUMAN MIND. 15S

trivances as the Ars Cornbinatoria and tlie Alphabet

of human thoughts, become interesting subjects of

philosophical discussion ; altliough the probability

is, that, even were that a;i'a to take place, they

would be found nearly as useless, in morals and poli-

tics, as the syllogistic art is acknowledged to be at

present in the investigations of pure geometry.

Of the peculiar and supereminent advantage pos-

sessed by mathematicians, in consequence of those

fixed and definite relations which form the objects

of their science, and the correspondent precision in

their language and reasonings, I can think of no

illustration more striking than what is afforded by

Dr Halley's Iâtin version from an Arabic manu-

script, of the two books of Appoilonius Pergasus de

Secftone Rationis. The extraordinary circumstan-

ces under which tliis version was attempted and

completed (which 1 presume are little known be-

yond the narrow circl'j of mathematical readers),

appear to me so liighly curious, considered as

matter of literary history, that I shall copy a short

detail of them from Halley's preface.

After mentioning the accidental discovery in the

Bodleian library, by Dr Bernard, Saviiian Professor

of Astronomy, of the Arabic version of Appoilonius,

7r.'pi Ao*)>a aTTOTOjw-Ji?, Dr Plalley proceeds thus :

*' Delighted, therefore, with the discovery of such

*' a treasure, Bernard applied himself diligently to

*' the task of a Latin translation. But before he

** had finished a tenth part of his undertaking, he

" abandoned it altogether, either from his experi-

*' ence of its growing difficulties, or from the pres-

154* ELEMENTS OF THE PHILOSOPHY Chap. II.

" sure of other avocations. Afterwards, when, on

*' the death of Dr Wallis, the Savilian professorship

" was bestowed on me, I was seized with a strong

" desire of making a trial to complete what Bernard

" had begun ;—an attempt, of the boldness of which

" the reader may judge, when he is informed, that,

" in addition to my own entire ignorance of the

" Arabic language, I had to contend with the ob-

" scurities occasioned by innumerable passages which

" were either defaced or altogether obliterated.

" With the assistance, however, of the sheets which

" Bernard had left, and which served me as a key

" for investigating the sense of the original, I began

*' first with making a list of those words, the signi-

" fication of which his version had clearly ascer-

*' tained ; and then proceeded, by comparing these

" words, wherever they occurred, with the train of

" reasoning in which they were involved, to decy-

" pher, by slow degrees, the import of the context

;

" till at last I succeeded in mastering the whole

" work, and in bringing my translation (without

" the aid of any other person) to the forai in which

" I now give it to the public." *

When a similar attempt shall be made, with equal

success, in decyphering a moral or a political trea-

tise, written in an unknown tongue, then, and not till

then^ may we think of comparing the phraseology of

these two sciences with the simple and rigorous lan-

guage of the Greek geometers ; or with the more

* AppoUon. Perg. de Seclione Rationis, &c. Opera et Studio

Edm. Halley. Oxon. 1706. In Frsfat.


refined and abstract, but not less scrupulously logi-

cal system of sigfis, employed by modern mathema-

ticians.

It must not, however, be imagined, that it is sole-

ly by the nature of the ideas which form the objects

of its reasonings, even when combined with the pre-

cision and unambiguity of its phraseology, that ma-

thematics is distinguished from the other branches

of our knowledge. The truths about which it is

conversant, are of an order altogether peculiar and

singular ; and the evidence of which they admit re-

sembles nothing, either in degree or in kind, to

which the same name is given, in any of our other

intellectual pursuits. On these points also, Leibnitz

and many other great men have adopted very incor-

rect opinions ; and, by the authority of their names,

have given currency to some logical errors of funda-

mental importance. My reasons for so thinking 1

shall state, as clearly and fully as I can, in the fol-

lowing section.

Section III.

Of Mathematical Demoiistration.

I.

Of the Ciraimstance on xvhich Demonstrative Evi-

dence essentialh) deimnds.

The peculiarity of that species of evidence which is

called demonstrative, and which so remarkably dis-

tinguishes our mathematical conclusions from those


to which we are led in other branches of science, is

a fact which must have arrested the attention of

every person wlio possesses the slightest acquaint-

ance with the elements of geometry. And yet I amdoubtful if a satisfactory account has been hitherto

given of the circumstances from which it arises. MrLocke tells us, that " what constitutes a demonstra-

*' tion is intuitive evidence at every step ;" and I

readily grant, that if, in a single step, such evidence

should fail, the other parts of the demonstration

would be of no value. It does not, however, seem

to me that it is on this consideration that the de-

monstrative evidence of the conclusion depends,

—

not even when we add to it another which is much

insisted on by Dr Reid,—that, '' in demonstrative

" evidence, our first principles must be intuitively

" certain." The inaccuracy of this remark I for-

merly pointed out when treating of the evidence of

axioms ; on which occasion I also observed, that the

first principles of our reasonings in mathematics are

not CLvioms, but definitions. It is in this last cir-

cumstance (I mean the peculiarity of reasoning from

definitionsJ that the true theory of mathematical

demonstration is to be found ; and I shall according-

ly endeavour to exphiin it at considerable length,

and to state some of the more important consequen-

ces to which it leads.

That I may not, however, have the appearance of

claiming, in behalf of the following discussion, an

undue share of originality, it is necessary for me to

remark, that the leading idea which it contains has

been repeatedly started, and even to a certain length


prosecuted, by different writers, ancient as well as

modern ; but that, in all of them, it has been so

blended with collateral considerations, altogether fo-

reign to the point in question, as to divert the at-

tention both of writer and reader, from that single

principle on which the solution of the problem

hinges. The advantages which mathematics de-

rives from the peculiar nature of those relations

about which it is conversant ; from its simple and

definite phraseology ; and from tlie severe logic so

admirably displayed in the concatenation of its in-

numerable theorems, are indeed immense, and well

entitled to a separate and ample illustration ; but

they do not appear to have any necessary connec-

tion with the subject of this section. How far I

am right in this opinion, my readers will be enabled

to judge by the sequel.

It was already remarked, in the first chapter of

tliis Part, that whereas, in all other sciences, the

propositions which we attempt to establish express

facts real or supposed,—in matliematics, the propo-

sitions which we demonstrate only assert a connec-

tion between certain suppositions and certain conse-

quences. Our reasonings, therefore, in mathema-

tics, are directed to an object essentially different

from what we have in view, in any other employ-

ment of our intellectual faculties ;—not to ascertain

truths with respect to actual existences, but to trace

the logical filiation of consequences which follow

from an assumed liypothesis. If from this hypothe-

sis we reason with correctness, nothing, it is mani-

fest, can be wanting to complete the evidence of the


result ; as this result only asserts a necessary con-

nection between the supposition and the conclusion.

In the other sciences, admitting that every ambigui-

ty of language were removed, and that every step of

our deductions were rigorously accurate, our conclu-

sions would still be attended with more or less of

uncertainty ; being ultimately founded on principles

which may, or may not, correspond exactly with the

flict.*

Hence it appears, that it might be possible, by

devising a set of arbitrary definitions, to form a

science which, although conversant about moral,

political, or physical ideas, should yet be as certain

as geometry. It is of no moment whether the defi-

nitions assumed correspond with facts or not, pro-

vided they d,.o not express impossibilities, and be

not inconsistent with each other. From these prin-

ciples, a series of consequences may be deduced by

the most unexceptionable reasoning ; and the re-

sults obtained will be perfectly analogous to mathe-

matical propositions. The terms true and Jcdse

cannot be applied to them ; at least in the sense in

which they are applicable to propositions relative to

* This distinction coincides with one which has been very in-

weniously illuîtratiid by INI. Prevost in his Philosophical Essays.

See his remarks on those sciences which have for their object

absolute truth, considered in contrast with, those which are occu-

pied only about conditional or Itypotlietical truths. INIathematics

is a science of the latter description ; and is therefore called by

M. Prevost a science of pure reasoning.— Essais de Philosophie,

Tom. II. p. 9. et seq. See also his Mtmoire sur les Signes. Paris,

Baudoin, 1800, pp. 15, l6. In what respects my opinion on

this subject differs from his, will appear afterwards.


facts. All that can be said is, that they are or are

not connected with the definitions which form the

principles of the science ; and, therefore, if we

choose to call our conclusions true in the one case,

a,nd Jhlse in the other, these epithets must be under-

stood merely to refer to their connection with the

data, and not to their correspondence with things

actually existing, or with events which we expect to

be realized in future. An example of such a science

as that which I have now been describing, occurs in

what has been called by some writers theoretical me-

chanics ; in which, from arbitrary hypotheses con-

cerning physical laws, the consequences are traced

which would follow, if such was really the order of

nature.

In those branches of study which are conversant

about moral and political propositions, the nearest

approach which I can imagine to a hypothetical

science, analogous to mathematics, is to be found in

a code of municipal jurisprudence ; or rather might

be conceived to exist in such a code, if systematically

carried into execution, agreeably to certain general

or fundamental principles. Whether these prin-

ciples should or should not be founded in justice and

expediency, it is evidently possible, by reasoning

from them consequentially, to create an artificial or

conventional body of knowledge, more systematical,

and, at the same time, more complete in all its parts,

than, in the present state of our information, any

science can be rendered, which ultimately appeals to

the eternal and immutable standards of truth and

falsehood, of right and wrong. This^ consideration

160 ELEMENTS OF THE PHILOSOPHY Chap. 11,

seems to me to throw some liglit on the following

very curious parallel which Leibnitz has drawn (with

what justness I presume not to decide) between the

works of the Roman civilians, and those of the Greek

geometers. Few writers certainly have been so ful-

ly qualified as he was to pronounce on the character-

istical merits of both.

" I have often said, that, after the writings of

*' geometricians, there exists nothing which, in point

*' of force and of subtilty, can be compared to the

" works of the Roman lawyers. And, as it would

*' be scarcely possible, from mere intrinsic evidence,

" to distinguish a demonstration of Euclid's fronr

" one of Archimedes or of Appollonius (the style

*' of all of them appearing no less uniform than if

*' reason herself was speaking through their organs),

*' so also the Roman lawyers all resemble each other

*' like twin-brothers ; insomuch that, from the style

" alone of any particular opinion or argument, hard-

*' ly any conjecture could be formed with respect to

*' the author. Nor are the traces of a refined and

" deeply meditated system of natural jurisprudence

*' anywhere to be found more visible, or in greater

" abundance. And, even in those cases where its

*' principles are departed from, either in compliance

" with the language consecrated by technical forms,

*' or in consequence of new statutes, or of ancient

*' traditions, the conclusions which the assumed

^ hypothesis renders it necessary to incorporate with

*' the eternal dictates of right reason, are deduced

*' with the soundest logic, and with an ingenuity

" which excites admiration. Nor are these devia-

Sect. 3. OF THE HUMAN MIND. I6l

" tions from the law of nature so frequent as is com-

" monly imagined." *

I have quoted this passage merely as an illustra-

tion of the analogy already alluded to, between the

systematical unity of mathematical science, and

that which is conceivable in a system of municipal

law. How far this unity is exemplified in the Ro-

man code, I leave to be detennined by more compe-

tent judges, t

As something analogous to the hypothetical br

conditional conclusions of mathematics may thus be

fancied to take place in speculations concerning mo-

ral or political subjects, and actually does take place

in theoretical mechanics ; so, on the other hand, if

a mathematician should affirm, of a general property

of the circle, that it applies to a particular figure de-

scribed on paper, he would at once degrade a geo-

metrical theorem to the level of a fact resting ulti-

mately on the evidence of our imperfect senses.

The accuracy of his reasoning could never bestow on

his proposition that peculiar evidence which is pro-

perly called mathematical, as long as the fact remain-

* Leibnitz, Op. Tom. IV. p. 254.

+ It is not a little curious, that the same code which furnished

to this very learned and philosophical jurist the subject of the

eulogium quoted above, should have been lately stigmatized by

an English lawyer, eminently distinguished for his acuteness and

originality, as '* an enormous mass of confusion and inconsisten-

" cy." Making all due allowances for the exaggerations of

Leibnitz, it is difficult to conceive that his opinion, on a subject

which he had so profoundly studied, should be so very widely at

variance with the truth.

VOL. II. L


ed uncertain, whether all the straight lines drawn

from the centre to the circumference of the figure

were mathematically equal.

These observations lead me to remark a very com-

mon misconception concerning mathematical defini-

tions, which are of a nature essentially different

from the definitions employed in any of the other

sciences. It is usual for writers on logic, after tak-

ing notice of the errors to which we are liable in

consequence of the ambiguity of words, to appeal

to the example of mathematicians, as a proof of the

infinite advantage of using, in our reasonings, such

expressions only as have been carefully defined. Va-

rious remarks to this pui-pose occur in the writings

both of Mr Locke and of Dr Reid. But the ex-

ample of mathematicians is by no means applicable

to the sciences in which these eminent philosophers

propose that it should be followed ; and, indeed, if

it were copied as a model in any other branch of hu-

man knowledge, it would lead to errors fully as dan-

gerous as any which result from the imperfections of

language. The real fact is, that it has been copied

much more than it ought to have been, or than

would have been attempted, if the peculiarities of

mathematical evidence had been attentively con-

sidered.

That in mathematics there is no such thing; as an

ambiguous word, and that it is to the proper use of

definitions we are indebted for this advantage, must

unquestionably be granted. But this is an advan-

tage easily secured, in consequence of the very li-

mited vocabulary of mathematicians, and the dis-

Sect. 3. OF THE HUBIAN MIND. 16S

tinctness of the ideas about which their reasonings

are employed. The difference, besides, in this re-

spect, between mathematics and the other sciences,

however great, is yet only a difference in degree5

and is by no means sufficient to account for the es-

sential distinction which every person must perceive

between the irresistible cogency of a mathematical

demonstration, and that of any other process of rea-

soning.

From the foregoing considerations it appears, that,

in mathematics, definitions answer two purposes

;

first. To prevent ambiguities of language ; and, se-

condly. To serve as the principles of our reasoning.

It appears further, that it is to the latter of these cir-

cumstances (I mean to the employment of hypothe-

ses instead of facts, as the data on which we proceed)

that the peculiar force of demonstrative evidence is

to be ascribed. It is, however, only in theformer use

of definitions, that any parallel can be drawn between

mathematics and those branches of knowledge which

relate to facts ; and, therefore, it is not a fair argu-

ment in proof of their general utility, to appeal to

the unrivalled certainty of mathematical science,—

a

pre-eminence which that science derives from a

source altogether different, though comprehended

under the same name, and which she will for ever

claim as her own exclusive prerogative. *

Nor ought it to be forgotten, that it is in pure

* These two classes of definitions are very generally confound-

ed by logicians; among others, by the Abbe de Condillac. See

La Logique, oil les premiers developpemens de V Art de Pcnser,

Chap. VI. 8

164 ELEMENTS OF THE PHILOSOPHY Chap. IL

mathematics alone, that definitions can be attempt-

ed with propriety at the outset of our investigations.

In most other instances, some previous discussion is

necessary to shew, that the definitions which we lay

down correspond with facts ; and, in many cases,

the formation of a just definition is the end to which

our inquiries are directed. It is very judiciously

observed by Mr Burke, in his Essay on Taste, that

" when we define, we are in danger of circumscrib-

*' ing nature within the bounds of our own notions,

" which we often take up by hazard, or embrace on

" trust, or form out of a limited and partial consider-

" ation of the object before us, instead of extending

** our ideas to take in all that nature comprehends,

*' according to her manner of combining. We are

*' limited in our inquiry by the strict laws to which

" we have submitted at our setting out."

The same author adds, that " a definition may** be very exact, and yet go but a very little way to-

" wards informing us of the nature of the thing de-

*' fined ;" and that, " in the order of things, a de-

" finition (let its virtue be what it will) ought ra-

" ther to follow than to precede our inquiries, of

" which it ought to be considered as the result."

From a want of attention to these circumstances,

and from a blind imitation of the mathematical ar-

rangement, in speculations where facts are involved

among the principles of our reasonings, numberless

errors in the writings of philosophers might be easi-

ly traced. The subject is of too great extent to be

pursued any further here ; but it is well entitled to

the examination of all who may turn their thoughts

i

Sect. 3. OF THE HUMAN MIND. l65

to the reformation of logic. That the ideas of Ari-

stotle himself, with respect to it, were not very pre-

cise, must, I think, be granted, if the following state-

ment of his ingenious commentator be admitted as

correct.

" Every general term," says Dr Gillies, '* is con-

" sidered by Aristotle as the abridgment of a defi-

*' nition ; and every definition is denominated by*' him a collection., because it is the result always of

" observation and comparison, and often of many ob-

" servations and of many comparisons." *

These two propositions will be found, upon ex-

amination, not very consistent with each other. The

first, " That every general term is the abridgment

" of a definition," applies, indeed, admirably to ma-

thematics ; and touches with singular precision on

the very circumstance which constitutes (in my opi-

nion) the peculiar cogency of mathematical reason-

ing. But it is to mathematics that it applies exclu-

sively. If adopted as a logical maxim in other

branches of knowledge, it would prove an endless

source of sophistry and error.—The second proposi-

tion, on the other hand, " That every definition is

" the result of observation and comparison, and of-

" ten of many observations and many comparisons ;"

however applicable to the definitions of natural his-

tory, and of other sciences which relate toJacts, can-

not, in one single instance, apply to the definitions

of geometry ; inasmuch as these definitions are nei-

ther the result of observations nor of comparisons^

* Gillies's Aristotle, Vol. I. p. 92, 2d edit.


but the hypotheses^ or first principles, on which the

whole science rests.

If the foregoing account ofdemonstrative evidence

be just, it follows, that no chain of reasoning what-

ever can deserve the name of a denlonstration (at

least in the mathematical sense of that word) which

is not ultimately resolvable into hypotheses or defini-

tions. * It has been already shewn, that this is the

case with geometry ; and it is also manifestly the?

case with arithmetic, another science to which, in

common with geometry, we apply the word mathe-

matical. The simple arithmetical equations 2 -]~ 2

=r 4 ; 2 -|- 3 — .5, and other elementary proposi-

tions of the same sort, are (as was formerly observ-

ed) mere definitions t ; perfectly analogous, in this

respect, to those at the beginning of Euclid ; and it

is from a few fundamental principles of this sort, or

* Although the account given by Locke of what constitutes a

demount rafiun, be different from that which I have here proposed,

he admits the converse of this doctrine as manifest ; viz. That if

we reason accurately from our own definitions, our conclusions

will po!ise$s demonstrative evidence; and, " hence," he observes

with great truth,- " it comes to pass, that one may often meet

" with very clear and coherent discourses, that amount yet to

" nothing." He afterwards remarks, that " one may make de-

" monstrations and undoubted propositions in words, and yet

*• thereby advance not one jot in the knowledge of the truth of

" things.'^ " Of this sort," he adds, " a man may find an in-

" finite number of propositions, reasonings, and conclusions, in

" books of metaphysics, school-divinity, and some sort of natural

'' philosoph}' ; and, after all, know as little of God, spirits, or

*' bodies, as lie did before he set out."—£way on Human Un-

derstonding. Book IV. chap»viii,

t See page 32.

Sect. 3. OF THE HUMAN MIND. l67

at least from principles which are essentially of the

same description, that all the more complicated re-

sults in tlie science are derived.

...To this general conclusion, with respect to the

nature of mathematical demonstration, an exception

may perhaps be, at first sight, apprehended to occur

in our reasonings concerning geometrical problems ;

all of these reasonings (as is well known) resting ul-

timately upon a particular class of principles called

postulates, which are commonly understood to be so

very nearly akin to axioms, that both might, with-

out impropriety, be comprehended under the same

name. " The definition of a postulate,*' says the

learned and ingenious Dr Hutton, " will nearly

*' agree also to an axiom, which is a self-evident the-

** orem, as a postulate is a self-evident problem." *

The same author, in another part of his work, quotes

^ remark from Dr Barrow, that *' there is the same

" affinity between postulates and problems, as be-

*' tween axioms and theorems." t Dr Wallis, too,

appears, from the following passage, to have had a

decided leaning to this opinion :" According to

" some, the difference between axioms and postu-

" lates is analogous to that between theorems and

" problems ; the former expressing truths which

" are self-evident, and from which other proposi-

" tions may be deduced ; the latter, operations

" which may be easily performed, and by the help

" of which more difficult constructions may be «f-

* IMathematical Dictionary, Art. Postulate.

t Ibid. Art. Hypothesis.


" fected.*' He afterwards adds, " This account

" of the distinction between postulates and axioms

" seems not ill adapted to the division of mathema-** tical propositions into problems and theorems.

" And, indeed, if both postulates and axioms were

" to be comprehended under either of these names,

" the innovation would not, in my opinion, afford

" much ground for censure." *

In opposition to these very high authorities, I

have no hesitation to assert, that it is with the defi-

nitions of Euclid, and not with the axioms^ that the

lyostulates ought to be compared, in respect of their

logical character and importance ;—inasmuch as all

the demonstrations in plane geometry are ultimate-

ly founded on the former, and all the constnictions

which it recognises as legitimate, may be resolved

ultimately into the latter. To this remark it may

be added, that, according to Euclid's view of the

subject, the problems of geometry are not less hypo-

thetical and speculative than the theorems ; the pos-

sibility of drawing a mathematical straight line, and

of describing a mathematical circle, being assumed

in the construction of every problem, in a wây quite

analogous to that in which the enunciation of a theo-

rem assumes the existence of straight lines and of

circles corresponding to their mathematical defini-

tions. The reasoning, therefore, on which the so-

lution of a problem rests, is not less demonstrative

than that which is employed in proof of a theorem.

Grant the possibility of the three operations describ-

* Wallisii Opera; Vol, II. pp. 667, 66S.

ggpj 3^ OF THE HUMAN MIND. l69

ed in the postulates, and the correctness of the solu-

tion is as mathematically certain, as the truth of any

property of the triangle or of the circle. The three

postulates of Euclid are, indeed, nothing more than

the definitions of a circle and a straight line throvm

into a form somewhat different ; and a similar re-

mark may be extended to the corresponding distri-

bution of propositions into theorems and problems.

Notwithstanding the many conveniences with which

this distribution is attended, it was evidently a mat-

ter of choice rather than of necessity ; al! the truths

of geometry easily admitting of being moulded into

either shape, according to the fancy of the mathe-

matician. As to the ajionSf there cannot be a

doubt (whatever opinion may be entertained of their

utility or of their insigniiicance) that they stand

precisely in the same relation to both classes of pro-

positions.*

* In farther illustration of what is said above, on the subject

of postulates and of problems, I transcribe, with pleasure, a short

passage from a learned and interesting memoir, just published,

by an author intimately and critically conversant with the clas-

sical remains of Greek geometry.

*' The description of any geometrical line from the data by

" which it is defined, must always be assumed as possible, and

*' is admitted as the legitimate means of a geometrical coustruc-

" tion : it is therefore properly regarded as a postulate. Thus,

" the description of a straight line and of a circle are the postu-

" lates of plane geometry assumed by Euclid. The description

" of the three conic sections, according to the definitions of them,

" must also be regarded as postulates ; and, though not formally

" stated like those of Euclid, are in truth admitted as huch b)

*' Apollonius, and all othei writers on this branch of geometry

" The same principle must be extended to all superior lines.


II.

Continuation of the Sul/ject.—Hotjo far it is true

that all Mathematical Evidence is resolvable in^

to Identical Propositions,

I HAD occasion to take notice, in the first section

of the preceding chapter, of a theoiy with respect to

the nature of mathematical evidence, very different

from that which I have been now attempting to ex-

plain. According to this theory (originally, I be-

lieve, proposed by Leibnitz) we are taught, that all

mathematical evidence ultimately resolves into the

perception of identity ; the innumerable variety of

propositions which have been discovered, or which

remain to be discovered in the science, being only

diversified expressions of the simple formula, a = a*A writer of great eminence, both as a mathemati-

" It is true, however, that the properties of such superior lines

*' may be treated of, and the description of them may be assumed

" in the solution of problems, without an actual delineation of

" them.' For it must be observed, that no lines whatever, not

" even the straight line or circle, can be truly represented to the

" senses according to the strict mathematical definitions ; but

*' this by no means affects the theoretical conclusions which are

" logically deduced from such definitions. It is only when geo-

" metry is applied to practice, either in mensuration, or in the

" arts connected with geometrical principles, that accuracy of

*' delineation becomes important."—See an Account of the Life

and Writings of Robert Simson, M. D. By the Rev. William

Trail, LL. D. Published by G. and W. Nicol, London, 1812.

* It is more than probable, that this theory was suggested to

Leibnitz by some very curious observations in Aristotle's Meta-

physics, Book IV. chap, iii. and jv.

?«Ct. 3. OF THE HUMAN MIND. 171

cian and a philosopher, has lately given his sanction,

in the strongest terms, to this doctrine ; asserting,

that all the prodigies performed by the geometrician

are accomplished by the constant repetition of these

words,

—

the same is the same. " Le geonietre

" avance de supposition en supposition. Et retour-

" nant sa pensee sous mille formes, c'est en repetant

** sans cesse, le meme est le meme, qu'il opere tons

" ses prodiges."

As this account of mathematical evidence appears

to me quite irreconcilable with the scope of the fore-

going observations,- it is necessary, before proceed-

ing farther, to examine its real import and amount

;

and what the circumstances are from which it de-

rives that plausibility which it has been so generally

supposed to possess. *

That all mathematical evidence resolves ultimate-

ly into the perception of identity, has been consider-

ed by some as a consequence of the commonly re-

ceived doctrine, which represents the axioms of Eu-

clid as ihejirst j^rinciples of all our subsequent rea-

* I must here observe, in justice to my friend M. Prevost, that

the two doctrines which I have represented in the above para-

graph as quite irreconcilable, seem to be regarded by him as not

only consistent with each other, but as little more than difterent

modes of stating the same proposition. The remarks with which

he has favoured me on this point will be found in the Appendix

annexed to this volume. At present, it may suffice to mention,

that none of the following reasonings apply to that particular

view of the question which he has taken. Indeed, I consider the

difterence of opinion between us, as to the subject now under con-

sideration, as chiefly verbal. On the subject of the preceding

article, our opinions are exactly the same. See Appendix.

172 ELEMENTS OF THE PHILOSOPHY CI *p. II.

sonings in geometry. Upon this view of the sub-

ject I have nothing to offer, in addition to what I

have ah'eady stated. The argument which I mean

to combat at present is of a more subtile and refined

nature ; and, at the same time, involves an admix-

ture of important truth, which contributes not a

little to the specious verisimilitude of the conclusion.

It is founded on this simple consideration, that the

geometrical notions of equality and of coincidence

are the same ; and that, even in comparing together

spaces of different figures, all our conclusions ulti-

mately lean, with their whole weight, on the imagi-

nary application of one triangle to another ;—the

object of which imaginary application is merely to

Ideyitifi) the two triangles together, in every circum-

stance connected both with magnitude and figure. *

Of the justness of the assumption on which this

argument proceeds, I do not entertain the slightest

* It was probably with a view to the establishment of this

doctrine, that some foreign elementary writers have lately given

the name of identical triangles to such as agree with each other,

both in sides, in angles, and in area. The differences which may

exist between them in respect of place, and of relative position

(differences which do not at all enter into the reasonings of the

geometer), seem to have been considered as of so little account

in discriminating them as separate objects of thought, that it has

been concluded they only form one and the same triangle, in the

contemplation of the logician.

This idea is very explicitly stated, more than once, by Ari-

stotle : lea oiv ro rrogov h. " Those things are ecjual whose quanti-

" ty is the same ;" (Met. iv. c. \6.) and still more precisely iij

these remarkable words, iv raroi? rj idori^g ivoTrig ;" In mathema-

" tical quantities, equality is identity." (Met. x. c. 3.)

For some remarks on this last passage, see Note (F.)

Sect. 3. OF THE HUMAN MIND. l?^

doubt. Whoever has the curiosity to examine any

one theorem in the elements of plane geometry, in

which different spaces are compared together, will

easily perceive that the demonstration, when traced

back to its first principles, terminates in the fourth

proposition of Euclid's first book : a proposition of

which the proof rests entirely on a supposed applica-

tion of the one triangle to the other. In the case of

equal triangles which differ in figure, this expedient

of ideal supei'position cannot be directly and imme-

diately employed to evince their equality ; but the

demonstration will nevertheless be found to rest at

bottom on the same species of" evidence. In illustra-

tion of this doctrine, I shall only appeal to the

thirty-seventh proposition of the first book, in which

it is proved that triangles on the same base, and be-

tween the same parallels, are equal ; a theorem which

appears, from a very simple construction, to be only

a few steps removed from the fourth of the same

book, in which the supposed application of the one

triangle to the other is the only medium of compa-

rison from which their equality is inferred.

In general, it seems to be almost self-evident, that

the equality of two spaces can be demonstrated only

by shewing, either that the one might be applied to

the other, so that their boundaries should exactly

coincide ; or that it is possible, by a geometrical con-

struction, to divide them into compartments, in such

a manner, that the sum of parts in tlie one may be

proved to be equal to the sum of parts in the other,

upon the principle of superposition. To devise the

easiest and simplest constructions for attaining this


end, is the object to which the skill and invention of

the geometer is chiefly directed.

Nor is it the geometer alone who reasons upon

this principle. If you wish to convince a person of

plain understanding, who is quite unacquainted with

mathematics, of the truth of one of Euclid's theo-

rems, it can only be done by exhibiting to his eye

operations exactly analogous to those which the

geometer presents to the understanding. A good

example of this occurs in the sensible or experimen-

tal illustration which is sometimes given of the forty-

seventh proposition of Euclid's first book. For this

purpose, a card is cut into the form of a right angled

triangle, and square pieces of card are adapted to the

dilFerent sides ; after which, by a simple and inge-

nious contrivance, the different squares are so dis-

sected, that those of the two sides are made to cover

the same space with the square of the hypothenuse.

In truth, this mode of comparison by a superposition,

actual or ideal, is the only test of equality which it

is possible to appeal to ; and it is from this (as seems

from a passage in Proclus to have been the opinion

of Apollonius) that, in point of logical rigour, the

definitioJi of geometrical equality should have been

taken. * The subject is discussed at great length,

* I do not think, however, that it would be fair, on this ac-

count, to censure Euclid for the arrangement which he has adopt-

ed, as he has thereby most ingeniously and dexterously contrived

to keep out of the view of the student some very puzzling ques-

tions, to which it is not possible to give a satisfactory answer till

a considerable progress has been made in the elements. When

iL is stated in the form of a self-evident truth, that magnitudes

which coincide, or which exactly fill the same space, are equal


and with much acuteness, as well as learning, in one

of the mathematical lectures of Dr Barrow ; to

which I must refer those readers who may wish to

see it more fully illustrated.

I am strongly inclined to suspect, that most of the

writers who have maintained that all mathematical

evidence resolves ultimately into the perception of

identity, have had a secret reference, in their own

minds, to the doctrine just stated ; and that they

have imposed on themselves, by using the words

identity and equality as literally synonymous and

convertible terms. This does not seem to be at all

consistent, either in point of expression or of fact,

with sound logic. When it is affirmed (for instance)

that, ** if two straight lines in a circle intersect each

** other, the rectangle contained by the segments of

to one another ; the beginner readily yields his assent to the pro-

position; and this assent, without going any farther, is all that

is required in any of the demonstrations of the first six books

:

\vhereas, if the proposition were converted into a definition, by

saying, " Equal magnitudes are those which coincide, or which*' exactly fill the same space ;" the question would immediately

occur, Are no magnitudes equal, but those to which this test of

e(|uality can be applied ? Can the relation of equality not subsist

between magnitudes which differ frem each other in figure?—In

reply to this question, it would be necessary to explain the de-

finition, by adding, That those magnitudes likewise are said to be

equal, which are capable of being divided or dissected in such a

manner that the parts of the one may severally coincide with the

parts of the other :—a conception much too refined and compli-

cated for the generality of students at their first outset; and

which, if it were fully and clearly a])prehendcd, would plunge

them at once into the profound speculation concerning the cojti-

parison of rectilinear with curvilinear figures.


" the one is equal to the rectangle contained by the

*' segments of the other j" can it with any propriety

be said, that the relation between these rectangles

may be expressed by the formula a = a? Or, to

take a case yet stronger, when it is affirmed, that

" the area of a circle is equal to that of a triangle

*' having the circumference for its base, and the ra-

*' dius for its altitude ;" would it not be an obvious

paralogism to infer from this proposition, that the

triangle and the circle are one and the same thing ?

In this last instance,* Dr Barrow himself has thought

it necessary, in order to reconcile the language of

Archimedes with that of Euclid, to have recourse to

a scholastic distinction between actual and jôtential

coincidence ; and, therefore, if we are to avail our-

selves of the principle of superpositio?!, in defence of

the fashionable theory concerning mathematical evi-

dence, we must, I apprehend, introduce a corre-

spondent distinction bet^veen actual and potential

identity. *

* " Cum demonstravil Archimedes circulum ajquari rectangu-

" lo triangulo cujus basis radio circuli, cathctus peripherite exce-

'* quetiir, nil illc, siquis propius attendat, aliud quicquara quam" arcam circuli ceu polygoni rcgularis indefinite multa lateraha-

" beiilis, ill totdividi posse minutissima triangula, quaj totidem ex-

" ilissimis dicti trianguli trigonis a?qucntur; eorum vero triangulo-

" rum aequalitas e sola congruciitia demonstratur in dementis

" Undo conscqu(Miter Archimedes circuli cum triangulo (sibi quan-

" tumvis dissimili) congruentiam dcmonstravit. Ita.congruentiae

" nihil obstat figurarum dissimilitudo ; verum seu similes sive dis-

" similes sint, mode cequales, semper poterunt, semper poss e de-

" bebunt congruerc. Igitur oclavum axioma vel nullo mode" convcrsum valet, aut universaliter convert! potest; nullo mo-

Sect. 3. OF THE HUMAN MIND, 177

That I may not be accused, however, of misre-

presenting the opinion which I am anxious to refute,

I shall state it in the words of an author, who has

made it the subject of a particular dissertation ; and

who appears to me to have done as much justice to

his argument as any of its other defenders.

*' Omnesmathematicorum propositiones sunt iden-

" ticae, et repraesentantur hac formula, a — a. Sunt

" veritates identicte, sub varia forma expressae, imo

" ipsum, quod dicitur contradictionis principium,

" vario modo enunciatum et involutum ; siquidem

" omnes hujus generis propositiones revera in eo

" continentur. Secundum nostram autem intelli-

*' gendi facultatem ea est propositionum differentia,

" quod quasdam longa ratiociniorum serie, alia autem

" breviore via, ad primum omnium principium redu-

*' cantur, et in illud resolvantur. Sic v. g. propo-

" sitio 2 + 2=4 statim hue cedit 1 + 1 + 1 + 1

" = 1 + 1 + 1 + 1 ; i. e. idem est idem ; et pro-

" prie loquendo, hoc modo enunciari debet.—Si

" contingat, adesse vel existere quatuor entia, turn

" existunt quatuor entia ; nam de existentia non

" agunt geometras, sed ea hypothetice tantum sub-

*• intelligitur. Inde summa oritur certitudo ratio-

" cinia perspicienti ; observat nempe idearum iden-

** titatem ; et haec est evidentia assensmn immediate-

" cogens, quam mathematicam aut geometricam vo-

" do, si quae isthic habetur congruentia designet actualem con*

" gruentiam ; universim, si de potentiali tantiim accipiatur."—

Lcctiones Mathematics, Lect. V.

VOL. II. M


" camus. Mathesi tamen sua natura priva non est

" et propria ; oritur etenim ex identitatis percep-

*' tione^ quae locum habere potest, etiamsi ideae non

" repraesentent extensum." *

With respect to this passage^ I have only to

remark, that the author confounds two things

essentially different ;—the nature of the truths

which are the objects of a science, and the na-

ture of the evidence by which these truths are

established. Granting, for the sake of argument,

that all mathematical propositions may be represent-

ed by the formula a = a, it would not therefore fol-

low, that every step of the reasoning leading to these

conclusions was a proposition of the same nature;

and that, to feel the full force of a mathematical

demonstration, it is sufficient to be convinced of this

maxim, that everything may he truly predicated of

itself; or, in plain English, that the sajne is the

same. A paper written in cypher, and the inter-

pretation of that paper by a skilful decypherer, may,

in like manner, be considered as, to all intents and

purposes, one and the same thing. They are so, in

fact, just as much as one side of an algebraical equa-

* The above CNtract (from a dissertation priiited at Bcilin in

1764) has long had a very extensive circulation in this country,

ill conbcqui'uct of its being quoted by Dr Beattie, in his Essay on

Truth, (see p. 22!, 2(1 edit.) As the learned author of the Essay

has not given the slightest intimation of his own opinion on the

subject, the doctrine in question has, I suspect, been considered

as in some measure sanctioned by his authority. It is only in

this way that I can account for the facility vvith which it has

been admitted by so many of our northern logicians.


tioii is the same thing with the other. But does it

therefore follow, that the whole evidence upon which

the art of decyphering proceeds resolves into the

perception of identity ?

It may be fairly questioned, too, whether it can,

with strict correctness, be said even of the simple

arithmetical equation 2 4-2 = 4, that it may be re-

presented by the formula a = a. The one is a pro-

position asserting the equivalence of ttvo dijferefit

compressions ;—to ascertain which equivalence may,

in numberless cases, be an object of the highest im-

portance. The other is altogether unmeaning and

nugatory, and cannot, by any possible supposition, ad-

mit of the slightest application of a practical nature.

What opinion, then, shall we form of the proposition

a = a, when considered as the representative of such

diformula as the binomial theorem of Sir Isaac New-

ton ? When applied to the equation 2-1-2 = 4

(which, from its extreme simplicity and familiarity,

is apt to be regarded in the light of an axiom), the

paradox does not appear to be so manifestly extrava-

gant ; but, in the other case, it seems quite impos-

sible to annex to it any meaning whatever. *

* The foregoing reasonings are not meant as a refutation of the

arguments urged by any one author in support of the doctrine in

question; but merely as an examination of those by which [

have either heard it defended, or from which I conceived that it

might possibly derive its verisimilitude in the judgment of those

who have adopted it. The arguments which I have supposed to

be alleged by its advocates, are so completely independent of

each other, that, instead of being regarded as different premises

leading to the same conclusion, they amount only to so many

different interpretations of the same verbal proposition ,—-•*.


I should scarcely have been induced to dwell so

long on this theory of Leibnitz concerning mathe-

matical evidence, if I had not observed among some

late logicians (particularly among the followers of

Condillac) a growing disposition to extend it to all

the different sorts of evidence resulting from the

various employments of our reasoning powers. Con-

dillac himself states his own opinion on this point

with the most perfect confidence. " Lêvidence de

" raison consiste uniquement dans Videntite : c'est

** ce que nous avons demontre. II faut que cette

" verite soit bien simple pour avoir echappe a tons

" les philosophes, quoiqu'ils eussent tant d'interet

" a s*assurer de Tevidence, dont ils avoient continu-

" ellement le mot dans la bouche.*' *

circumstance which, I cannot help thinking, affords of itself no

slight proof, that this proposition has been commonly stated in

terms too general and too ambiguous for a logical principle.

What a strange inference has been drawn from it by no less a

philosopher than Diderot !" Intcrrogez des mathematiciens de

" bonne foi, et ils vous avoueront que leurs propositions sont

" toutes identiques, et que tant de volumes sur le cercle, par ex-

" emple, se reduisent h nous repeter en cent mille fagons diffe-

" rentes, que c'est une figure ou toutes les lignes tirees du centre

" k la circonfereiice sont egales. Nous ne savons done presque

" nm,"—Lettre sur les Aveugles.

* La Logique, Chap, IX.

On another occasion, Condillac expresses himself thus :" Tout

" le systeme des connoissances humaines pent etre rendu par une

" expression plus abregee et tout-a-fait identique : les sensations

" so7tt des sensations. Si nous pouvions, dans toutes les sciences,

" suivre egalemcnt la generation des idees, et saisir le vrai sys-

*• t^me des choses, nous verrions d'une verity naitre toutes les


The demonstration here alluded to is extremely

concise ; and if we grant the two data on which it

proceeds, must be universally acknowledged to be ir-

resistible. The first is, " Tliat the evidence of

" every mathematical equation is that of identity :"

The second, " That what are called, in the other

**^ sciences, projwsitioiis or judgments^ are, at bot-

" torn, precisely of the same nature with equa-

*' tions.*'—But it is proper, on this occasion, to let

our author speak for himself.

" Mais, dira-t-on, c'est ainsi qu'on raisonne en

" mathematiques, ou le raisonnement se fait avec

" des equations. En sera-t-il de meme dans les au-

** tres sciences, ou le raisonnement se fait avec des

** propositions ? Je reponds qu' equations^ proposi-

" tions, JugemenSf sont au fond la meme chose, et

*' que par consequent on raisonne de la meme mani-*' ere dans toutes les sciences." *

Upon this demonstration I have no comment to

offer. The truth of the first assumption has been

already examined at sufficient length ; and the se-

cond (which is only Locke's very erroneous account

ofjudgment^ stated in terms incomparably more ex-

ceptionable) is too puerile to admit of refutation.

It is melancholy to reflect, that a writer who, in his

earlier years, had so admirably unfolded the mighty

influence of language upon our speculative conclu-

sions, should have left behind him, in one of his

" auties, et nous trouverions I'expression abregee de tout ce que" nous saurions, dans cette proposition identioue : le meme est le

" meme."

* La Logiqiiej Chap. VIII.

182 ELEMENTS OF THE PHILOSOPHY Chap. II-

latest publications, so memorable an illustration of

his own favourite doctrine.

It was manifestly with a view to the more com-

plete establishment of the same theory, that Con-

dillac undertook a work, which has appeared since

his death, under the title of La Langue des Cal-

euls ; and which, we are told by the editors, was on-

ly meant as a prelude to other labours, more inte-

resting and more difficult. From the circumstances

which they have stated, it would seem that the in-

tention of the author was to extend to all the other

branches of knowledge, inferences similar to those

which he has here endeavoured to establish with re-

spect to mathematical calcidations ; and much re-

gret is expressed by his friends, that he had not

lived to accomplish a design of such incalculable im-

portance to human happiness. I believe I may safe-

ly venture to assert, that it was fortunate for his re-

putation he proceeded no farther ; as the sequel

must, from the nature of the subject, have affi)rded,

to every competent judge, an experimental and pal-

pable proof of the vagueness and fallaciousness of

those views by which the undertaking was suggested.

In his posthumous volume, the mathematical preci-

sion and perspicuity of his details appear to a su-

perficial reader to reflect some part of their own

light on the general reasonings with which they are

blended ; while, to better judges, these reasonings

come recommended with many advantages and with

much additional authority, from their coincidence

with the doctrines of the Leibnitzian school.

It would probably have been not a little mortify-


ing to this most ingenious and respectable pliiloso-

plier, to have discovered, th<it, in attempting to ge-

neralize a very celebrated theory of Leibnitz, he had

stumbled upon an obsolete conceit, started in this

island upwards of a century before. " When a man" reasoneth," says Hobbes, " he does nothing else

" but conceive a sum total, from addition of parcels ;

*' or conceive a remainder from subtraction of one

" sum from another ; which (if it be done by words)

** is conceiving of the consequence of the names of

** all the parts, to the name of the whole ; or from

** the names of the whole and one part, to the name*' of the other part.—These operations are not inci-

** dent to numbers only, but to all manner of things

" that can be added together, and taken one out of

" another.—-In sum, in what matter soever there is

" place for addition and subtraction, there also is

" place for reason ; and where these have no place,

" there reason has nothing at all to do.

" Out of all which we may define what that is

*' which is meant by the word ?'easo7iy when we*' reckon it amongst the faculties of the mind. For

** reasoUf in this sense, is nothing but reckoning

** (that is, adding and subtracting) of the conse-

" quences of general names agreed upon, for the

" ma?'kmg and signijying of our thoughts ;—I say

** marking them, when we reckon by ourselves;

" and signifying, when we demonstrate, or approve

" our reckonings to other men." *

Agreeably to this definition, Hobljes has given te

* r.evialliaHj Chap. V,

184 ELEMENTS OF THE PHILOSOPHY Chap. It.

the first part of his elements of philosophy the title

of CoMPUTATio, sive LoGiCA ; evidently employ-

ing these two words as precisely synonymous. From^

this tract I shall quote a short paragraph, not certain-

ly on account of its intrinsic value, but in conse-

quence of the interest which it derives from its coin-

cidence with the speculations of some of our con-

temporaries. 1 transcribe it from the Latin edition,

as the antiquated English of the author is apt to

puzzle readers not familiarized to the peculiarities

of his philosophical diction.

" Per ratiocinationem autem intelligo computa-

" tionem. Computare vero est plurium rerum" simul additariim summam colligere^ vel imd re ab

" alia detractd^ cognoscere residuum. Ratiocinari

*' igitur idem est quod addere et subtrahere, vel si

** quis adjungat his midtiplicare et dividere, non*' abnuam, cum multiplicatio idem sit quod aequali-

" um additioy divisio quod ffiqualium quoties fieri

" potest subtractio. Recidit itaque ratiocinatio

" omnis ad duas operationes animi, additionem et

" subtractio7iem.'* * How wonderfully does this jar-

gon agree with the assertion of Condillac,thatall equ-

ations are propositions, and all propositions equations

!

* The Logica of liobbes has been lately translated into French,

under the title of Calculi ou Logique, by M. Destutt-Tracy. It

is annexed to the third volume of his Elemens d'Ideologie, where

it is honoured with the highest eulogies by the ingenious transla-

tor. " L'ouvrage en masse," he observes in one passage, " merite

" d'etre regarde comme un praduit precieux des meditations de

" Bacon et de Descartes sur le systeme d'Aristote, et corame le

" gernie des progres ultericures de la science."—-Disc. FriL

p. 117.

Sect 3. OF THE Human mind* 185"

These speculations, however, of Condillac and of

Hobbes relate to reasoning in general ; and it is

with mathematical reasoning alone that we are im-

mediately concerned at present. That the peculiar

evidence with which this is accompanied is not re-

solvable into the perception of identity, has, I flatter

myself, been sufficiently proved in the beginning of

this article ; and the plausible extension by Con-

dillac of the very same theory to our reasonings in

all the different branches of moral science, affords a

strong additional presumption in favour of our con-

clusion.

From this long digression, into which I have been

insensibly led by the errors of some illustrious foreign-

ers concerning the nature of mathematical demon-

stration, I now return to a further examination of

the distinction between sciences which rest ulti-

mately on facts, and those in which definitions or hy-

fotheses are the sole principles of our reasonings.

Ill,

Continuation of the Subject,—Evidence of the Me-chanical Philosophy^ not to be confounded with

that tvhich is properly called Demonsttâtive or

Mathematical.—Opposite Error of some late

Writers.

Next to geometry and arithmetic, in point of

evidence and certainty, is that branch of general

physics which is now called mechanical philosophyj

r—a science in which the progress of discovery has


been astonishingly rapid, during the course of the

last century ; and which, in the systematical conca-

tenation and filiation of its elementary principles,

exhibits every day more and more of that logical

simplicity and elegance which we admire in the

works of the Greek mathematicians. It may, I think,

be fairly questioned, whether, in this department of

knowledge, the affectation of mathematical method

has not been already carried to an excess ; the essen-

tial distinction between mechanical and mathema-

tical truths being, in many of the physical systems

wliich have lately appeared on the Continent, studi-

ously kept out of the reader's view, by exhibiting

both, as nearly as possible, in the same form. Avariety of circumstances, indeed, conspire to iden-

tify in the imagination, and, of consequence, to assi-

milate in the mode of their statement, these two

very different classes of propositions ; but as this

assimilation (beside its obvious tendency to involve

experimental facts in metaphysical mystery) is apt

occasionally to lead to very erroneous logical conclu-

sions, it becomes the more necessary, in proportion

as it arises from a natural bias, to point out the

causes in which it has originated, and the limitations

with which it ought to be understood.

The following slight remarks will sufficiently ex-

plain my general ideas on this important article of

logic.

1. As the study of the mechanical philosophy is,

in a great measure, inaccessible to those who have

not received a regular mathematical education, it

Sect. 3. OF THE HUMAn^ MIND. 187

commonly happens, that a taste for it is, in the first

instance, grafted on a previous attachment to the re-

searches of pure or abstract mathematics. Hence a

natural and insensible transference to physical pur-

suits, of mathematical habits of thinking ; and hence

an almost unavoidable propensity to give to the for-

mer science that systematical connection, in all its

various conclusions, which, from the nature of its

first principles, is essential to the latter, but which

can never belong to any science which has its founda-

tions laid in facts collected from experience and

observation.

2. Another circumstance, which has co-operated

powerfully with the former in producing the same

effect, is that proncness to simplification which has

misled the mind, more or less, in all its researches;

and which, in natural philosophy, is peculiarly en-

couraged by those beautiful analogies which are ob-

servable among different physical phenomena ;—ana-

logies, at the same time, which, however pleasing to

the fancy, cannot always be resolved by our reason

into one general law. In a remarkable analogy, for

example, wiiich presents itself between the equality

of action and re-action in the collision of bodies, and

what obtains in their mutual attractions, the coinci-

dence is so perfect, as to enable us to comprehend all

the various facts in the same theorem ; and it is difficult

to resist the temptation which this theorem seems to

offer to our ingenuity, of attempting to trace it, in

both cases, to some common principle. Such trials

of theoretical skill I would not be understood to cen-

sure indiscriminately ; but, in the present instance, I

188 ELEMENTS of TflE PHILOSOPHY Chap. II.

am fully persuaded, that it is at once more unexcep-

tionable in point of sound logic, and more satisfacto-

ry to the learner, to establish the fact, in particular

cases, by an appeal to experiment ; and to state the

law of action and re-action in the collision of bodies,

as well as that which regulates the mutual tenden-

cies of bodies towards each other, merely as general

rules which have been obtained by induction, and

which are found to hold invariably, as far as our

knowledge of nature extends. *

* It is observed by Mr Robison, in his Elements of Mecha-

nical Philosophy, that " Sir Isaac Newton, in the general scho-

*' liuni on the laws of motion, seems to consider the equality of

*' action and re-action, as an axiom deduced from the relations

*' of ideas. But this," says Mr Robison, " seems doubtful. Be-

" cause a magnet causes the iron to approach towards it, it does

" not appear that we necessarily suppose that iron also attracts

" the magnet." In confirmation of this he remarks, that not-

withstanding the previous conclusions of Wallis, Wren, and

Huyghens, about the mutual, equal, and contrary action of solid

bodies in their collisions, " Newton himself only presumed, that

" because the sun attracted the planets, these also attracted the

" sun ; and that he is at much pains to point out phenomena to

" astronomers, by which this maybe proved, when the art of ob-

" servation shall be sufficiently perfected." Accordingly, Mr Ro-

bison, with great propriety, contents himself with stating this

third law of motion, as a fact " with respect to all bodies on

" which we can make experiment or observation fit for deciding

** the question."

In the very next paragraph, however, he proceeds thus :" As

" it is an universal law, we cannot rid ourselves of the pcrsua-

" sion that it depends on some general principle which influences

*' all the matter in the universe;"—to which observation he sub-

joins a conjecture or hypothesis concerning the nature of this

principle or cause. For an outline of his theory I must refer I©

Sect. 3. ®F THE HUMAN MIND. 18f)

An additional example may be useful for the il-

lustration of the same subject. It is well known to

be a general principle in mechanics, that when, by

means of any machine, two heavy bodies counteqjoise

each other, and are then made to move together,

the quantities of motion with which one descends,

and the other ascends perpendicularly, are equal.

This equilibrium bears such a resemblance to the case

of two moving bodies stopping each other, when

they meet together with equal quantities of motion,

that, in the opinion of many writers, the cause of an

equilibrium in the several machines is sufficiently ex-

plained, by remarking, *' that a body always loses as

" much motion as it communicates.'* Hence it is

his own statement.—See Elements of Mechanical Philosophy,

Vol. I. pp. 1'24, 125, 126

Of the fallaciousness of synthetical reasonings concerning

physical phenomena, there cannot be a stronger proof, than the

diversity of opinion among the most eminent philosophers with

respect to the species of evidence on which the third law of mo-

tion rests. On this point, a direct opposition may be remarked

in the views of Sir Isaac Newton, and of his illustrious friend and

<:omraentator, Mr Maclaurin ; the former seeming to lean to the

supposition, that it is a corollary deduct ble a priori from abstract

principles ; while the latter (manifestly considering it as the ef-

fect of an arbitrary arrangement) strongly recommends it to the

attention of those who delight in the investigation of final causes.*

My own idea is, that, in the present state of our knowledge, it is

at once more safe and more logical to consider it merely as aa

experimental truth ; without venturing to decide positively on

either side of the question. As to the doctrine of final causes,

it fortunately stands in need of no aid from such dubious specu-

lations.

* Account of Newtou's Philosophical Discoveries. Book II. Chap. *.

J 28.


inferred, that when two heavy bodies are so circum-

stanced, that one cannot descend without causing

the other to ascend at the same time, and with the

same quantity of motion, both of these bodies must

necessarily continue at rest. But this reasoning,

however plausible it may seem to be at first sight, is

by no means satisfactory ; for (as Dr Hamilton has

justly observed *) when we say, that one body com-

municates its motion to another, we must suppose

the motion to exist, first in the one, and afterwards

in the other ; whereas, in the case of the machine,

the ascent of the one body cannot, by any conceiv-

able refinement, be ascribed to a communication of

motion from the body which is descending at the

same moment ; and, therefore (admitting the truth

of the general law which obtains in the collision of

bodies), we might suppose, that in the machine, the

superior weight of the heavier body would overcome

the lighter, and cause it to move upwards with the

same quantity of motion with which itself moves

downwards. In perusing a pretended demonstra-

tion of this sort, a student is dissatisfied and puz-

zled ; not from the difficulty of the subject, which is

obvious to every capacity, but from the illogical

and inconclusive reasoning to which liis assent is re-

quired, t

* See Philosophical Essays, by Hugh Hamilton, D. D. Pro-

fessor of Phi]oso|)hy in the University of Dublin, p. 135, et scq.

3d edit. (London, 1772.)

+ The following observation of Dr Hamilton places this ques-

tion in its true point of view. " However, as tlie theorem above

" mentioned is a very elegant one, it ought certainly to be taken

Sect. 3. OF THE HUMAN MIND. IQl

3. To these remarks it may be added, that even

when one proposition in natural philosophy is logi-

cally deducible from another, it may frequently be

expedient, in communicating the elements of the

science, to illustrate and confirm the consequence, as

well as the principle, by experiment. This I should

apprehend to be proper, wherever a consequence is

inferred from a principle less familiar and intelligi-

ble than itself; a thing which must occasionally

happen in physics, from the complete incorporation

(if I may use the expression) which, in modern

times, has taken place between physical truths, and

the discoveries of mathematicians. The necessary

effect of this incorporation was, to give to natural

philosophy a mathematical form, and to systematize

its conclusions, as far as possible, agreeably to rules

suggested by mathematical method.

In pure mathematics, where the truths which we

investigate are all co-existent in point of time, it is

universally allowed, that one proposition is said to

be a consequence of another, only with a reference

" notice of in every treatise of mechanics, and may serve as a

" very good index of an (equilibrium in all machines ; but I do

" not think that we can from thence, or from any one general

" principle, explain the nature and effects of all the mechanic

" powers in a satisfactory manner."

To the same purpose, it is remarked by Mr Maclaurin, that

" though it be useful and agreeable to observe how uniformly

" this principle prevails in engines of every sort, throughout the

*' whole of mechanics, in all cases where an equilibrium takes

'* place; yet that it would not be right to rest the evidence of

** so important a doctrine upon a proof of this kind only."—y/c-

count of Neictori's Discoveries, B. II. c. 3.


to our established arrangements. Thus all the pro-

perties of the circle might be as rigorously deduced

from any one general property of the curve, as from

the equality of the radii. But it does not therefore

follow, that all these arrangements would be equally

convenient : on the contrary, it is evidently useful,

and, indeed, necessary, to lead the mind, as far as

the thing is practicable, from what is simple to what

is more complex. The misfortune is, that it seems

impossible to carry this rule universally into execu-

tion : and, accordingly, in the most elegant geome-

trical treatises which have yet appeared, instances

occur, in which consequences are deduced from prin-

ciples more complicated than themselves. Such in-

versions, however, of what may justly be regarded

as the natural order, must always be felt by the au-

thor as a subject of regret ; and, in proportion to

their frequency, they detract both from the beauty

and from the didactic simplicity of his general de-*

sign.

The same thing often happens in the elementary

doctrines of natural philosophy. A very obvious

example occurs in the different demonstrations given

by writers on mechanics, from the resolution of

forces, of the fundamental proposition concerning

the lever;—demonstrations in which the proposition,

even in the simple case when the directions of the

forces are supposed to be parallel, is inferred from a

process of reasoning involving one of the most refin-

ed principles employed in the mechanical philoso-

phy. I do not object to this arrangement as illogi-

10


cal ; nor do I presume to say that it is injudicious. *

I would only suggest the propriety, in such instances,

* In some of these demonstrations, however, then- is a logical

inconsistency so glaring, that I cannot resist the ti mptation of

pointing it out here, as a good instance of that undue predilection

for mathematical evidence, in the exposition of physical prin-

ciples, which is conspicuous in many elementary treatises. I al-

lude to those demonstrations of the property of the lever, in

which, after attempting to prove the general theorem, on the

supposition that the directions of the forces meet in a point, the

same conclusion is extended to the simple case in which these

directions are parallel, by the fiction (for it deserves no other

name) of conceiving parallel lines to meet at an infinite distance,

or to form with each other an angle infinitely small. It is strange,

that such a proof sliould ever have been thought more satisfacto-

ry than the direct evidence of our senses. How much more

reasonable and pleasing to begin with the simpler case (which

may be easily brought to the test of experiment J, and then to

deduce from it, by the resolution of forces, the general proposi-

tion ! Even Dr Hamilton himself, who has treated of the mecha-

nical powers with much ingenuity, seems to have imagined, that,

by demonstrating the theorem, in all its cases, from the composi-

tion and resolution of forces alone, he had brought the whole

subject within the compass of pure geometry. It could scarcely,

however (one should think), have escaped him, that every valid

demonstration of the composition of forces must necessarily as-

sume as a fact, that " when a body is acted upon by a force pa-

" rallel to a straight line given in position, this force has no effect

" either to accelerate or to retard the progress of the body to-

" wards that line." Is riot this fact much farther removed from

common observation than the fundamental property of the lever,

which is familiar to every peasant, and even to every savage ?

And yet the same author objects to the demonstration of Huy-

ghens, that it depends upon a principle, iKhich (he says) ought not

to be granted on this occasion,— that " when two equal bodies are

" placed on the arms of a lever, that which is furthest from thie

*^fulcrum will preponderate."

VOL. II. N -

I94f ELEMENTS OF THE PHILOSOPHY Chap, II.

of confirming and illustrating the conclusion, by an

appeal to experiment ; an appeal which, in natural

philosophy, possesses an authority equal to that which

is generally, but very improperly, considered as a

mathematical demonstration of physical truths. In

pure geometiy, no reference to the senses can be ad-

mitted, but in the way of illustration ; and any such

reference, in the most trifling step of a demonstra-

tion, vitiates the whole. But, in natural philoso-

phy, all our reasonings must be grounded on prin-

ciples for which no evidence but that of sense can

be obtained ; and the propositions which we es-

tablish differ from each other only as they are de-

duced from such principles immediately, or by the

intervention of a mathematical demonstration. Anexperimental proof, therefore, of any particular

physical truth, when it can be conveniently obtain-

ed, although it may not always be the most elegant

or the most expedient way of introducing it to the

knowledge of the student, is as rigorous and as sa-

tisfactory as any other ; for the intervention of a

process of mathematical reasoning can never bestow

on our conclusions a greater degree of certainty tlian

our principles possessed. *

* Several of the foregoing remarks were sutrgested by certain

peculiarities of opinion relative to the distinct provinces of expe-

rimental and of mathematical evidence in the study of physics,

which were entertained by my learned and excellent friend, the

late Mr Robison. Though himself a most enlightened and zeal-

ous advocate for the doctrine of final causes, he is well known t»

have formed his scientific taste chiefly upon the mechanical phi-

losophers of the Continent, and, in consequence of this circum-

stance, to have undervalued experhnent, wherever a possibility

Stct.3. OF THE HUMAN MIND. 195

I have been led to enlarge on these topics by that

unqualified application of mathematical method to

physics, which has been fashionable for many years

past among foreign writers ; and which seems to

have originated chiefly in the commanding influence

which the genius and learning of Leibnitz have so

lono- maintained over the scientific taste of most

European nations. * In an account, lately publish-

ofi'ered of introducing mathematical, or even metaphysical reason-

ing. Of this bias various traces occur, both in his Elements of

INIechanical Philosophy, and in the valuable articles which he

furnished to the Encyclopajdia Britannica.

* The following very extraordinary passage occurs in a letter

from Leibnitz to INIr Oldenburg.

" Ego id agere constitui, ubi primum otium nactusero, utrem

" omnern mechanicam reducam ad puram geometriam ; proble-

*' mataque circa eiateria, et aquas, et pendula, et projecta, et so-

" lidorum resistcntiam, et frictiones, &c. definiam. Quae hac-

" tenus attigit nemo. Credo autem rem oranem nunc esse in

" potestate ; ex quo circa rcgulas motuum raihi penitus perfec-

" tis demonstratiouibus satisfeci ; neque quicquam amplius in eo

" genere desidero. Tota autem res, quod raireris, pendetex axi-

" ornate metaphysico pulcherrimo, quod non minoris momenti** est circa motum, quam hoc, totum esse majus parte, circa mag-*' mtud'incm."—-Jrallisii Opera, Vol. III. p. 633.

The beautiful metaphysical axiom here referred to by Leibnitz,

is plainly the principle of the sufficient reason ; and it is not a lit-

tle remarkable, that the highest praise which he had to bestow

upon it was, to compare it to Euclid's axiom, " That the whole

" is greater than its part." Upon this principle of the sufficient

reason, Leibnitz, as is well known, conceived tLat a complete sys-

tem of physical science might be built, as he thought the whole

of mathematical science resolvable into the principles of identity

and of contradiction.—By the first of these principles (it may not

be altogether superfluous to add) is to be understood the maxim,

" Whatever is, is ;" By the second, the maxim, that " It is im-

" possible for the same thing to be, and not to be :"—two maxims


ed, of the Life and Writings of Dr Raid, I have

taken notice of some other inconveniences resulting

which, it is evident, are only different expressions of the same

proposition.

In the remarks made by Locke on the logical inutility of ma-

tketnaticat axioms, and on the loiiical danger of assuming meta-

physical axioms as the principles of our rt-asonings in other scien-

ces, 1 think it highly probable, that he had a secret reference to

the philosophical writings and epistolary correspondence of

Leibnitz This appears to ire to furnish a key to some of

Locke's observations, the scope of whicfi Dr Reid professes his

inabilit}^ to discover. One sentence, in particular, in which he

has animadverted with soiiie sev( rity, is, in my opinion, distinct-

ly pointed at the letter to Mr Oldenburg, quoted in the begin-

ning of this note.

" Mr Locke farther says (I borrow Dr Rcid's own statement),

" that maxims are not of use to help men forward iir the ad-

" vancement of the sciences, or new discoveries of yet unknown

" truths : that Newton, in the discoveries he has made in his

" never enough to be admired book, has not been assisted by the

" general maxim, whatever is, is ; or the whole is greater than a

" part, or the like."

As the letter to Oldenburg is dated in I676 (twelve years be-

fore the publication of the Essay on Human Understanding), and

as Leibnitz expresses a desire that it may be communicated to

Mr Newton, there can scarcely be a doubt that Locke had read

it; and it reflects infinite honour on his sagacity, that he seems,

at that early period, to have foreseen the extensive influence

which the errors of this illustrious man were so long to main-

tain over the opinions of the learned world. The truth is, that

even then he prepared a reply to some reasonings which, at the

distance of a century, were to mislead, both in physics and in lo-

gic, the first philosophers in Europe.

If these conjectures be well founded, it must be acknowledgecf

that Dr Reid has not only failed in his defence oi' maxims against

Locke's attack, but that he has totally misapprehended the aim

of Locke's argument. 3

Sect. 3. OF THE HUMAN MIND. 19?

from it, still more important than the introduction

of an unsound logic into the elements of natural

philosojjhy ; in particular, of the obvious tenden-

cy which it has to withdraw the attention from that

unity of design which it is the noblest employment

of philosophy to illustrate, by disguising it under

the semblance of an eternal and necessary order,

similar to what the mathematician delights to trace

among the mutual relations of quantities and figures.

The consequence has been (in too many physical

systems), to level the study of nature, in point of

moral interest, with the investigations of the alge-

braist ;—an effect, too, which has taken place most

" I answer." says lio, in tlie paragraph immediately following

that which was quoud above, " ihe first of these maxims (what-

" ever is, is) is an idoiUital proposition, of no use in mathema-

" tics, or in any otlier science. The- second (that the whole is

" greater than a part) is often used by Newton, and by ail

" mathematicians, and many demonstrations rest upon it.

" In general, Newton, as well as all other mathematicians,

*' grounds his demonstrations of mathematical propositions upon

" the axioms laid down by Euclid, or upon prnpositions which

" have been before demonstrated by lielp of these axioms.

'* But It deserves to be particularly observed, that Newton, in-

" tending in the third book of his Fiincipia to give a more scien-

" titic foim to the physical part of astronomy, which he had at

'* first composed ni a popukr form, thought proper to follow the

" example of Euclid, and to lay down first, in what he calls Re-

" gid(S Philosophandi, and in his Phenomena, the first principles

" which he assumes in his reasoning,

" Nothing, therefore, could, have been more unluckily adduced

" by Mr Locke to support his aversion to first principles, than

" the example of Sir Isaac Newton."

—

Essays on the Inf. Powers,

pp. 647, 648, 4to edit.

198 ELEMENTS OF THE PHILOSOPHY Chap. 11-

remarkably, where, from the sublimity of the sub-

ject, it was least to be expected,—in the applica-

tion of the mechanical philosophy to the phenomena

of the heavens. But on this very extensive and im-

portant topic I must not enter at present.

In the opposite extreme to the error which I have

now been endeavouring to correct, is a paradox

which was broached, about twenty years ago, by the

late ingenious Dr Beddoes ; and which has since

been adopted by some writers, whose names are bet-

ter entitled, on a question of this sort, to give weight

to their opinions. * By the partisans of this new

doctrine it seems to be imagined, that—so far from

physics being a branch of mathematics,—mathema-

tics, and more particularly geometry, is, in reality,

only a branch of physics. " The mathematical sci-

** ences," saysDr Beddoes, *' are sciences of experi-

** ment and observation, founded solely on the in-

*' duction of particular facts ; as much so as me-

" chanics, astronomy, optics, or chemistry. In the

" kind of evidence there is no diiference ; for it ori-

" ginates from perception in all these cases alike;

" but mathematical experiments are more simple,

" and more perfectly within the grasp of our senses,

* I allude here more particul.irly to my learned friend, Mr

Leslie, whose high and justly merited reputation, both as a ma-

thematician and an experimentalist, renders it indispensably ne-

cessary for me to take notice of some fundamental logical mis-

takes which he appears to me to have committed in the course

of those ingenious excursions, in \\ hich he occasionally indulges

himself, beyond the strict limits of his favourite studies.

4


" and our perceptions of mathematical objects are

** clearer."*

A doctrine essentially the same, though expres-

sed in terms not quite so revolting, has been lately

sanctioned by Mr Leslie ; and it is to his view of

the argument that I mean to confine my attention

at present. " The whole structure of geometry,"

he remarks, " is grounded on the simple comparison

" of triangles ; and all the fundamental theorems

" which relate to this comparison, derive their evi-

" dence from the mere superposition of the triangles

*' themselves ; a mode of proof which, in reality, is

*' nothing but an ultimate appeal, though of the

" easiest and most familiar kind, to external obser-

" vation.'* t And, in another passage : " Geo-

* Into this train of thinking, Dr Bcddocs informs us, he was

first led by Mr Home Tooke's speculations concerning language.

" In whatever study you are engaged, to leave difficulties behind

" is distressing : and when these difficulties occur at your very

" entrance upon a science, professing to be so clear and certain

" as geometry, your feelings become still more uncomfortable;

" and you are dissatisfied with j-our own powers of comprehen-

" sion. I therefore think it due to the author of EHEA riTE*

" POENTA, to acknowledge my obligations to him for relieving

" me from this sort of disti ess. For although I had often made*' the attempt, I could never solve certain difiiculties in Euclid,

" till my reflections were revived and assisted by Mr Tooke's dis-

" coveriesJ'—See Observations on the Nature of Demonstrative

Evidence. London, 1793, pp. 5 and 15.

f Elements of Geometry and of Geometrical Analysis, &c.

By Mr Leslie. Edinburgh, I8O9.

The assertion that the whole structure of geometry is founded

on the Comparison of triangles, is expressed in terms too unqua-

lified, D'Alembert has mentioned another principle as not less


" nietry,like the other sciences which arenot concern-

" ed about the operations of mind, rests ultimately on** external observations. But those ultimate facts

" are so few, so distinct and obvious, that the sub-

" sequent train of reasoning is safely pursued to un-

** limited extent, without ever appealing again to

" the evidence of the senses." *

Before proceeding to make any remarks on this

theory, it is proper to premise, that it involves two

separate considerations, which it is of material con-

sequence to distinguish from each other. The first

is, that extension and figure (the subjects of geo-

fundamcntal, the measurement of angles by circular arches.

" Les propositions ibndamentales de geometrie pcuvent eUe re-

*' duites a deux ; la mcsure des angles par les arcs de cercle, et

" le principe de la superposition."

—

Elemens de Philosophie, Art.

Geomttrie. The same writer, however, justly observes, in ano-

ther part of his works, that the measure of angles by circular

arches, is itself dependent on the principle of superposition ; and

that, consequently, however extensive and important in its appli-

cation, it is entitled only to rank with what he calls prindples of

a seco7td order. " La mesure des angles par les arcs de cercle

*' decrit de leur sommet, est elle-meme dependante du principe

" de la superposition. Car quand on dit que la mesure d'un an-

" gle est Tare circulaire decrit de son sommet, on veut dire que

*' si deux angles sont egaux, les angles decrits de leur sommet a

" memc rayon, seront egaux ; verite qui se demontre par le prin-

" cipe de la superposition, coniuie tout geometre tant soit peu

*' initie dans cette science le sentira facilemenl."

—

Eclaircisse-

mcns sur les Elemens de P/iilosop/iie, § iv.

Instead, therefore, of saying that the whole structure of geo-

metry is grounded on the comparison of triangles, it would be more

correct to say, that it is grounded on the principle of superpo-

sition.

* Elements of Geometry and of Geometrical Analysis, p. 453.

Feet. 3. OF THE HUMAN MIND. 201

metry) arc qualities of body which are made known

to us by our external senses alone, and which actual-

ly fall under the consideration of the natural phi-

losopher as well as of the mathematician. The se-

cond, that the whole fabric of geometrical science

rests on the comparison of triangles, in forming

which comparison, we are ultimately obliged to ap-

peal (in the same manner as in establishing the first

principles of physics) to a sensible and experimental

proof.

1. In answer to the first of these allecrations, it

might perhaps be sufficient to observe, that in order

to identify two sciences, it is not enough to state,

that they are both conversant about the same objects

;

it is necessary farther to shew, that, in both cases,

these objects are considered in the same point of

view, and give employment to the same faculties of

the mind. The poet, the painter, the gardener,

and the botanist, are all occupied in various degrees

and modes, with the study of the vegetable king-

dom;

yet who has ever tliought of confounding

their several pursuits under one connnon name ?

The natural historian, the civil historian, the moral-

ist, the logician, the dramatist, and the statesman,

are all engaged in the study of man, and of the

principles of human nature; yet how widely discri-

minated are these various departments of science and

of art ! how different are the kinds of evidence on

which they respectively rest ! how different the in-

tellectual habits which they have a tendency to

fonii ! Indeed, if this mode of generalization were

to be admitted as legitimate, it would lead us to


blend all the objects of science into one and the

same mass ; inasmuch as it is by the same impres-

sions on our external senses, that our intellectual

faculties are, in the first instance, roused to action,

and all the first elements of our knowledge un-

folded.

In the instance, however, before us, there is a

very remarkable specialty, or rather singularity,

which renders the attempt to identify the objects of

geometrical and of physical science, incomparably

more illogical than it would be to classify poetry

with botany, or the natural history of man with the

political history of nations. This specialty arises

from certain peculiarities in the metaphysical nature

of those sensible qualities which fall under the con-

sideration of the geometer ; and which led me, in

a different work, to distinguish them from other

sensible qualities (both primary and secondary), by

bestowing on them the title of mathematical affec-

tions of matter* Of these mathematical affections

Cmagnitude and JigureJ^ our first notions are, no

doubt, derived (as well as of hardness, softness,

roughness, and smoothness) from the exercise of our

external senses ; but it is equally certain, that when

the notions of magnitude and figure have once been

acquired, the mind is immediately led to consider

them as attributes of space no less than of body ;

and (abstracting them entirely from the other sensi-

ble qualities perceived in conjunction with them)

becomes impressed with an irresistible conviction,

* Philosophical Essays, pp. \)\, 05. 4lo edit.

Sect. 3. OP THE HUMAN MIND.

that their existence is necessary and eternal, and that

it would remain unchanged if all the bodies in the

universe were annihilated. It is not our business

here to inquire into the origin and grounds of this

conviction. It is with the fact alone that we are

concerned at present ; and this I conceive to be one

of the most obviously incontrovertible which the

circle of our knowledge embraces. Let those ex-

plain it as they best can, who are of opinion, that all

the judgments of the human understanding rest ulti-

mately on observation and experience.

Nor is this the only case in which the mind forms

conclusions concerning space, to which those of the

natural philosopher do not bear the remotest analogy.

Is it from experience we learn that space is infinite ?

or (to express myself in more unexceptionable

tenns), that no limits can be assigned to its immen-

sity ? Here is a fact, extending not only beyond the

reach of our personal observation, but beyond the

observation of all created beings ; and a fact on

which we pronounce with no less confidence, when

in imagination we transport ourselves to the utmost

verge of the material universe, than when we con-

fine our thoughts to those regions of the globe

which have been explored by travellers. How un-

like those general laws which we investigate in

physics, and which, how far soever we may find

them to reach, may still, for anything we are able

to discover to the contrary, be only contingent, lo-

cal, and temporary

!

It must indeed be owned, with respect to the con-

clusions hitherto mentioned on the subject of space.

1^04 ELEMENTS OF THE PHILOSOPHY Chap. II.

that tliey are rather of a metaphysical than of a ma-

thematical nature ; but they are not, on that ac-

count, the less applicable to our purpose ; for if the

theory of Beddoes had any foundation, it would

lead us to identify with physics the former of these

sciences as well as the latter ; at least, all that part

of the former which is employed about space or ex-

tension,—a favourite object of metaphysical as well

as of mathematical speculation. The truth, how-

ever, is, that some of our metaphysical conclusions

concerning space are more nearly allied to geometri-

cal theorems than we might be disposed at first to

apprehend ; being involved or implied in the most

simple and fundamental propositions which occur in

Euclid's Elements. When it is asserted, for exam-

ple, that " if one straight line falls on two other

" straight lines, so as to make the two interior an-

*' gles on the same side together equal to two right

" angles, these two straight lines, though indefi-

*' nitely produced, will never meet ;"—is not the

boundless immensity of space tacitly assumed as a

thing unquestionable ? And is not a universal affir-

mation made with respect to a fact which experience

is equally incompetent to disprove or to confirm ?

In like manner, when it is said, that *' triangles on

" the same base, and between the same parallels, are

*' equal,'* do we feel ourselves the less ready to give

our assent to the demonstration, if it should be sup-

posed, that the one triangle is confined within the

limits of the paper before us, and that the other,

standing on the same base, has its vertex placed be-

yond the sphere of the fixed stars ? In various in-


stances, we ai'e led, with a force equally imperious,

to acquiesce in conclusions, which not only admit of

no illustration or proof from the perceptions of sense,

but which, at first sight, are apt to stagger and con-

found the faculty of imagination. It is sufficient to

mention, as examples of this, the relation between

the hj'perbola and its asymptotes ; and the still

more obvious truth of the infinite divisibility of ex-

tension. What analogy is there between such pro-

positions as these and that which announces, that

the mercury in the Torricellian tube will fall, if

carried up to the top of a mountain ; or that the

vibrations of a pendulum of a given length will be

performed in the same time, while it remains in the

same latitude? Were there, in reality, that analogy

between mathematical and physical propositions which

Beddoes and his followers have fancied, the equality

of the square of the hypothenuse of a right angled

triangle to the squares described on the two other

sides, and the proportion of 1, 2, 3, between the

cone and its circumscribed hemisphere and cylinder,

might, with fully as great propriety, be considered

in the light of physical phenomena, as of geome-

trical theorems : Nor would it have been at all in-

consistent with the logical unity of his work, if MrLeslie had annexed to his Elements of Geometry,

a scholium concerning the final causes of circles and

of straight lines, similar to tliat v.'hich, with such

sublime effect, closes the Principia of Sir Isaac

Newton. *

* In the course of my own experience, I have met with one

person, of no common ingenuity, who seemed seriously disposed

<

S06 ELEMENTS OF THE PHILOSOPHY Cbap. If..

2. It yet remains for me to say a few words upon

that superposition of triangles which is the ground-

to considei" the truths of geometry very nearly in this light. The

person I allude to was James Ferguson, author of the justly po-

pular works on Astronomy and Mechanics. In the year 176S, he

paid a visit to Edinburgh, when I had not only an opportunity

of attending his public course of lectures, but of frequently en-

joying, in private, the pleasure of his very interesting conversa-

tion. I remember distinctly to have heard him say, that he had

more than once attempted to study the Elements of Euclid ; but

found himself quite unable to enter into that species of reason-

ing. The second proposition of the first book, he mentioned par-

ticularly as one of his stumbling-blocks at the very outset ;—the

circuitous process by which Euclid sets about an operation which

never could puzzle, for a single moment, any man who had seen

a pair of compasses, appearing to him altogether capricious and

ludicrous. He added, at the same time, that as there were va-

rious geometrical theorems of which he had dail)' occasion to make

use, he had satisfied himself of their truth, either by means of

his compasses and scale, or by some mechanical contrivances of

his own invention. Of one of these I have still a perfect recol-

lection ;—his mechanical or experimental demonstration of the

47th proposition of Euclid's first Book, by cutting a card so as to

afford an ocular proof, that the squares of the two sides actually

filled the same space with the square of the hypothcnuse.

To those who reflect on the disadvantages under which MrFerguson had laboured in point of education, and on the early

and exclusive hold which experimental science had taken of his

mind, it will not perhaps seem altogether unaccountable, that

the refined and scrupulous logic of Euclid should have struck

him as tedious, and even unsatisfactory, in comparison of that

more summary and palpable evidence on which his judgment was*

accustomed to rest. Considering, however, the great number of

years which have elapsed since this conversation took place, I

should have hesitated about recording, solely on my own testi-

mony, a fact so singular with respect to so distinguished a man,

if I had not lately found, from Dr Hutlon's Mathematical Die

Sect. 3. OF THE HUMAN MIND. 20^

work of all our geometrical reasonings concerning

the relations which different spaces bear to one

another in respect of magnitude. And here I must

take the liberty to remark, in the first place, that

the fact in question has been stated in terms much

too loose and incorrect for a logical argument.

When it is said, that " all the fundamental theo-

" rems which relate to the comparison of triangles,

" derive their evidence from the mere superposition

" of the triangles themselves," it seems difficult, or

rath^ impossible, to annex to the adjective mere an

idea at all different from what would be conveyed,

if the word actual were to be substituted in its place ;

more especially, when we attend to the assertion

which immediately follows, that *' this mode of proof

•* is, in reality, nothing but an ultimate appeal,

" though of the easiest and most familiar kind, to

^' external observation." But if this be, in truth,

the sense in which we are to interpret the statement

quoted above (and I cannot conceive any other in-

tionary, that he also had heard from jNIr Ferguson's mouth, the

most important of those particulars which I have now stated ;

and of which my own recollection is probably the more lively

and circumstantial, in consequence of the very early period of

my life when they fell under my notice.

" Mr Ferguson's general mathematical knowledge," says Dr

Hutton, " was little or nothing. Of algebra he understood little

" more than the notation ; and he has often told me he could

" never demonstrate one proposition in Euclid's Elements ; his

" constant method being to satisfy himself, as to the trutli of any

" problem, with a measurement by scale and compasses."

—

Mutton's Mathematical and Philosophical Dictionary, Article Fer-

^08 ELEMENTS OF THE PHILOSOPHY Cliap. II.

terpretation of which it admits), it must appear ob-

vious, upon the slightest reflection, that the state,

ment proceeds upon a total misapprehension of the

principle of superposition ; inasmuch as it is not to

an actual or mere superposition, but to an imaginary

or ideal one, that any appeal is ever made by the

geometer. Between these two modes of proof the

difference is not only wide, but radical and essential.

The one would, indeed, level geometry with physics,

in point of evidence, by building the whole of its

reasonings on a fact ascertained by mechanical mea-

surement : The other is addressed to the under-

standing, and to the understanding alone, and is as

rigorously conclusive as it is possible for demonstra-

tion to be. *

* The same remark was, more than fifty years ago, made by

D'Alembert, in reply to some mathematicians on the Continent,

who, it would appear, had then adopted a paradox very nearly

approaching to that which I am now combating. " Le principe

" de la superposition n'est point, comme I'ont pretendu plusieurs

" geometres, une niethode de demontrer peu exacte et purement

" mechanique. La superposition, telle que les mathemaliciens

" la con5oivent, ne consiste pas ^ appliquer grossierement une

" figure sur une autre, pour juger par les yeux de leur egalite

" ou de leur difference, comme un ouvrier applique son pie sur

" uneligne pour la mesurer ; elle consiste a imaginer une figure

" transportee sur une autre, et h. conclure de l'egalit6 supposee

" de certaines parties de deux figures, la coincidence de ces par-

" ties entr'elles, et de leur coincidence la coincidence du reste :

" d'ou rfesulte I'egaiite et la similitude pariaites des figures en-

" litres."

About a century before the time when D'Alembert wrote these

observations, a similar view of the subject was taken by Dr Bar-

row; a writer who, like D'Alembert, added to the skill and ori-

ginality of an inventive mathematician, the most refined, and, at


That the reasoning employed by Euclid in proof

of the fourth proposition of his first book is com-

pletely demonstrative, will be readily granted by

those who compare its different steps with the con-

clusions to which we were formerly led, when treat-

ino; of the nature of mathematical demonstration.

In none of these steps is any appeal made to Jacts

resting on the evidence of sense, nor, indeed, to any

Jacts whatever. The constant appeal is to the defi-

nition of equality. * " Let the triangle ABC,*' says

the same time, the justest ideas concernina; the theory of those in-

tellectual processes which are subservient to mathematical reason*

ing.—" Unde raeriio vir acutissimus Willebrordus Snellius lucu-

" lentissimum appellat geometrise supeliectilis instrumentum hanc

*' ipsam sfa^.actr/i'. Earn igitur in danonstrationibusmathematicis qui

''fastidiunt et respuunt, ut mechaniccB crassitudinis acaurn^yiag ali-

*' quid redolentcm, ipsissimam geometrice basin labefactare student

;

" ast imprudenler etfrustra. Nam i(pa^.u,o(Siv geometraj suam non

" manu sed mente peragunt, non oculi sensu, sed animi judicio

" aestimant. Supponunt (id quod nulla manus praestare, nulius

" scnsus disccrnere valet) accuratam et perfectam congrueiitiam,

" ex eaque supposita justas et logicas eliciunt consequentias.

" Nulius hic regulas, circini, vel norniy usus, nulius brachiorum

" labor, aut latrrum conteiitio, rationis totum opus, artificium et

" machinatio est; nil mechanicara sapiens auwy/af exigitur;

" nil, inquam, mechanicum, nisi quatenus omnis magnitudo sit

" aliquo mndo materiae inyoluta, sensibus exposita, visibilis et

*' palpabilis, sic utquod mens intelligi jubet, iil manus quadan-

•' tenus exequi possit, tt conlcmplationem praxis utcunque cone-

" tur aemulari. Qu^ tamen imitatio gf ometnca; demonstratio-

" nis robur ac dignitatem nedum non inhrmat aut deprimit, at

" validius constabilit, et atollit altius," &c.

—

Lectiones Mathana-

ticce. Led. III.

* It was before observed (see p. 174), that Euclid's eighth

VOL, II. O


Euclid, " be applied to the triangle D E F ; the point

" A to the point D, and the straight line A B to the

" straight line D E ; the point B will coincide with

" the point E, because A B is equal to D E, And** A B coinciding with D E, A C itill coincide with

*' D F, because the angle B A C is equal to the

** an(j!:le E D jP." A similar remark will be found

to apply to every remaining step of the reasoning ;

and, therefore, this reasoning possesses the peculiar

characteristic which distinguishes mathematical evi-

dence from that of all the other sciences,—^that it

rests wholly on hypotheses and dejinitions, and in no

respect upon any statement of facts, true or false.

The ideas, indeed, of extension, of a triangle, and

of equality, presuppose the exercise of our senses.

Nay, the very idea of superposition involves that of

motion^ and, consequently (as the parts of space are

immoveable), of a material triangle. But where is

there anything analogous, in all this, to those sen-

sible facts, which are the principles of our reasoning

in physics ; and which, according as they have been

accurately or inaccurately ascertained, determine the

accuracy or inaccuracy of our conclusions ? The ma-

terial triangle itself, as conceived by the mathema-

tician, is the object, not of sense, but of intellect.

axiom {magnitudes 'which coincide uith each other are equal)

ought, in point of logical rigour, to have been stated in the form

of a definition. In our present argument, however, it is not of

material consequence whether this criticism be adopted or not.

Whether we consider the proposition in question in the light of

an axiom or of a definition, it is equally evident, that it does not

express ajact ascertained by observation or by experiment.


It is not an actual measure, liable to expansion or

contraction, from the influence of heat or of cold

;

nor does it require, in the ideal use which is made

of it by the student, the slightest address of hand or

nicety of eye. Even in explaining this demonstra-

tion, for the first time, to a pupil, how slender so-

ever his capacity might be, I do not believe that any

teacher ever thought of illustrating its meaning by

the actual application of the one triangle to the other.

No teacher, at least, would do so, who had fonned

correct notions of the nature of mathematical science.

If the justness of these remarks be admitted, the

demo7istration in question must be allowed to be as

well entitled to the name, as any other which the

mathematician can produce ; for as our conclusions

relative to the properties of the circle (considered in

the light of hypothetical theorems) are not the less

rigorously and necessarily true, that no material

circle may anywhere exist corresponding exactly to

the definition of that figure, so the proof given by

Euclid of the fourth proposition would not be the

less demonstrative, although our senses were incomii

parably less acute than they are, and although no

material trian<2:le continued of the same magnitude

for a single instant. Indeed, when we have once

acquired the ideas of equality and of a common mea-

sure, our mathematical conclusions would not be in

the least affected, if all the bodies in the universe

should vanish into nothing.

To many of my readers, I am perfectly aware,

the foregoing remarks will be apt U) c«,v,pear tedious

and superfluous. My only apology for the length

î^ ELEMENTS OF THE PHILOSOPHY Chap. II.

to which they have extended is, my respect for the

talents and learning of some of those writers who

have lent the sanction of their authority to the logi-

cal errors which I have been endeavouring to cor-

rect ; and the obvious inconsistency of these conclu-

sions with the doctrine concerning the characteris-

tics of mathematical or demonstrative evidence,

which it was the chief object of tliis section to es-

tablish. *

* This doctrine is concisely and clearly stated by a writer

whose acute and orifrinal, though very eccentric genius, seldom

fails to redeem his wildest paradoxes by the new lights which he

strikes out in defending them, " Demoi.stratio est syllogisraus

*' vel syllogismorum series a nominum d' finitionibus usque ad

" conclusionem ultimam derivala."

—

Cumpufatio sive Logica,

cap. 6.

It will not, I trust, be inferred, from my having adopted, in

the words of Hobbes, this detached proposition, that lam disposed

to sanction any one of those conclusions which have been com-

monly SMp;)05PC? to be connected with it, in the mind of the au-

thor :—I say supposed, because I am by no means satisfied (not-

withstanding the loose and unguarded manner in which he has

stated some of his logical oj)inions) that justice has been done to

his views and motives in this part ot his workj.. My own notions

on the subject of evidence in general will be sufficiently unfolded

in the progress of roy speculations. In the meantime, to prevent

the possibility of any misapprehension of my meaning, I think

it proper once more to remark, that the definition of Hobbes,

quoted above, is to be understood (according to my interpreta-

tion of it) as applying solely to the word demonstration in pure

mathematics. The extension of the same term by Dr Clarke

and others, to reasonings which have for their object, not condi-

tional or hypothetical, but al'solute truth, appears to me to have

been attended with many serious inconveniences, which these ex-

cellent authors did not foresee. Of the demonstrations with

Sect. 4. OF THE HUMAN MIND. ^1^

Section IV.

Ofour Reasonings concerning Probable or Contin-

gent Truths.

I.

'Narroxo Field of Demonstrative Evidence.—OfDemonstrative Evidence^ when combined with

that of Sense, as in Practical Geometry ; and

with those of Sense and o/'iNDUCTiOxNf, as in the

Mechanical Philosophy.—Remarks on a Funda-

mental Law of Belief, involved in all our Rett'

sonings concerning Contingent Truths.

If the account which has been given of the nature

of demonstrative evidence be admitted, the province

vvhich Aristotle has attempted to fortify his syllogistic rules, I

shall afterwards have occasion to examine the valiility.

The charge of unlimited sceplicisra brought against Hobbes

has, in my opnii(jn, bet n occasioned partly by his neglecting to

draw the line between absolute and hypothetical truth, and partly

by his applying the word demonstration to our reasonings in other

sciences as well as in inatht-raatics. To these causes may perhaps

be added, the offence which his logical writings must have given

to the Realists of his time.

It is not, however, to Realists alone that the charge has been

confined. Leibnitz himseli has given some countenance to it, in

a dissertation prefixed to a work of Marius Nizulius ; ami Bruck-

er, in referring to this dissertation, has aggravated not a little the

censure of liobbes, which it seems to contain. " Quin si illus-

" trrm Leilmitzium au'timus, iiobbesius quoque inter nominales

"retercndus est, earn ob causam, quod ipso Occamo nominalior,

" rerum veritatem dicat in nominibus consisten , ac, quod majus

" est, pendere ab arbitrio humano."

—

Histor, Ptnlosop/i. de Idds,

p. 209. AugustEe Vindelicorum, 1723.

Sl^ ELEMENTS OF THE PHILOSOPHY Chap. II.

over which it extends must be limited almost entire-

ly to the objects of pure mathematics. A science

perfectly analogous to this, in point of evidence, may,

indeed, be conceived (as I have already remarked)

to consist of a series of propositions relating to mo-

ral, to political, or to physical subjects ; but as it

could answer no other purpose than to display the

ingenuity of the inventor, hardly anything of the

kind has been hitherto attempted. The only excep-

tion which I can think of occurs in the speculations

formerly mentioned, under the title of theoretical

mechanics.

But, if the field of mathematical demonstration be

limited entirely to hypothetical or conditional truths,

whence (it may be asked) arises the extensive and

the various utility of mathematical knowledge, in our

physical researches, and in the arts of life ? The an-

swer, I apprehend, is to be found in certain peculi-

arities of those objects to which the suppositions of

the mathematician are confined ; in consequence of

which peculiarities, real combinations of circumstan-

ces may fall under the examination of our senses,

approximating far more nearly to what his definitions

describe, than is to be expected in any other theore-

tical process of the human mind. Hence a corre-

sponding coincidence betv/een his abstract conclu-

sions, and those facts in practical geometry and in

physics which they help him to ascertain.

For the more complete illustration of this subject,

it may be observed, in the first place, that although

the peculiar force of that reasoning which is proper-

ly called mathematical, depends on the circumstance

1'


of its principles being hypothetical^ yet if, In any in-

stance, the supposition could be uscertalned as actu-

ally existing, the conclusion might, with the very

same certainty, be applied. If I were satisfied, for

example, that in a particular circle drawn on paper,

all the radii were exactly equal, every property

which Euclid has demonstrated of that curve might

be confidently affirmed to belong to this diagram.

As the thing, however, here supposed is rendered

impossible by the imperfection of our senses, the

truths of geometry can never, in their practical ap-

plications, possess demonstrative evidence ; but only

that kind of evidence which our organs of percep-

tion enable us to obtain.

But although, in the practical applications of pia-

thematics, the evidence of our conclusions differs es-

sentially from that which belongs to the truths in-

vestigated in the theory, it does not therefore fol-

low, that these conclusions are the less important.

In proportion to the accuracy of our data will be that

of all our subsequent deductions ; and it fortunate-

ly happens, that the same imperfections of sense

which limit what is physically attainable in the for-

mer, limit also, to the very same extent, what is

practically useful in the latter. The astonishing

precision which the mechanical ingenuity of modern

times has given to mathematical instruments has,

in fact, communicated a nicety to the results of prac-

tical geom.etry, beyond the ordinary demands of hu-

man life, and far beyond the most sanguine anticipa-

tions of our forefathers. *

* See a very interesting and able article, in the fifth volume


This remarkable, and, indeed, singular coinci-

dence of propositions purely hypothetical, with facts

which fall under the examination of our senses, is

owing, as I already hinted, to the peculiar nature of

the objects about which mathematics is conversant

;

and to the opportunity which we have (in conse-

quence of that mensurability * which belongs to all

of the Edinburgh Review, on Colonel Mudge's account of thfe

operations carried on for accomplishing a trigononiolrical survey

of England and Wales. I cannot deny mybclf the pleasure of

quoting a few sentences.

" In two distances that were deduced from sets of triangles,

" the one measured by General Roy in ]787, the other bylNIajor

" Mudge in 1794., one of 24.133 miles, and the other ot 38.688,

*' the two measures agree wilhiu a foot as to the first distance,

" and l6 inches as to the sectmd. Such an agreement, where

" the observers and the instruments were both different, where

" the lines measured were of such extent, and deduced from such

" a variety of aata^ is probably without any other example.

" Coincidences of this sort are frequent in the trigonometrical

*' survey, and prove how much more good instruments, used by

" skilful and attentive observers, are capable of performing, than

" the most sanguine theorist could have ever ventured to fore-

« tel.—

" It is curious to compare the early essays of practical geome-

" try with the perfection to which its operations have now reach-

" ed, and to consider that, while the artist had made so little

" progress, the theorist had reached many of the sublimest

" blights of mathematical speculation ; that the latter Lad found

" out the area of the circle, and calculated its circumference to

" more than a hundred places of decimals, when the former

" could hardly divide an arch into minutes of a degree ; and that

" many excellent treatises had been written on the properties of

" curve lines, before a straight line of considerable length had

" ever been careluUy drawn, or exactly measured on the sur-

" face ot the earth."

* See note (G.)

Seel. 4. or THE HUMAN MIND. Sl7

of them) of adjusting, with a degree of accuracy ap-

proximating nearly to the truth, the da/a from which

we are to reason in our practical operations, to those

which are assumed in our theory. The only affec-

tions of matter which these objects comprehend are

extension and figure ; affections wiiich matter pos-

sesses in common w ith space, and which may, there-

fore, be separated in fact, as well as abstracted in

thought, from all its other sensible qualities. In ex-

amining, accordingly, the relations of quantity con-

nected wdth these affections, we are not lia,ble to be

disturbed by those physical accidenU^ which, in- the

other applications of mathematical science, necessa-

rily render the result, more or less, at variance with

the theory. In measuring the height of a moun-

tain, or in the survey of a country, if we are at due

pains in ascertaining our data, and if wê reason from

them with mathematical strictness, the result may be

depended on as accurate within very narrow limits ;

and as there is nothing but the incorrectness of our

data by which the result can be vitiated, the limits

of possible error may themselves be assigned. But,

in the simplest applications of mathematics to me-

chanics or to physics, the abstractions which are ne-

cessary in the theory must always leave out circum-

stances which are essentially connected with the ef-

fect. In demonstrating, for example, the property

of the lever, we abstract entirely from its own

weight, and consider it as an inflexible mathemati-

cal line ;—suppositions with which the fact cannot

possibly correspond ; and for which, of course, al-

lowances (which nothing but physical experience

218 ELEIHENTS OF THE PHILOSOPHY Chap. IT.

can enable us to judge of) must be made in prac-

tice.*

Next to practical geometry, properly so called,

one of the easiest applications of mathematical theo-

ry occurs in those branches of optics which are dis-

tinguished by the name of catoptrics and dioptrics.

In these, the physical principles from which we rea-

son are few and precisely definite, and the rest of

the process is as purely geometrical as the Elements

of Euclid.

In that part of astronomy, too, which relates sole-

ly to the phenomena, without any consideration of

physical causes, our reasonings are purely geometri-

cal. The data, indeed, on which we proceed must

have been previously ascertained by obsei'vation ;

but the inferences we draw from these are connected

with them by mathematical demonstration, and are

accessible to all who are acquainted with the theoiy

of spherics.

In physical astronomy,- the law of gravitation be-

comes also a principle or datum in our reasonings

;

but as in the celestial phenomena, it is disengaged

from the effects of the various other causes which

are combined with it near the surface of our planet,

this branch of physics, as it is of all the most sub-

lime and comprehensive in its objects, so it seems,

in a greater degree than any other, to open a fair

and advantageous field for mathematical ingenuity.

In the instances which have been last mentioned,

the evidence of our conclusions resolves ultimately

* See Note (H.)

Stct. 4. OF THE HUMAN MIND. 219

not only into that of sense, but into another law of

belief formerly mentioned ; that which leads us to

expect the continuance, in future, of the established

order of physical phenomena. A very striking

illustration of this presents itself in the computations

of the astronomer ; on the faith of which he pre-

dicts, with the most perfect assurance, many cen-

turies before they happen, the appearances which

the heavenly bodies are to exhibit. The same fact

is assumed in all our conclusions in natural philoso-

phy ; and something extremely analogous to it in all

our conclusions concerning human affairs. They

relate, in both cases, not to necessary connections,

but to probable or contingent events ; of which

(how confidently soever we may expect them to take

place) the failure is by no means perceived to be

impossible. Such conclusions, therefore, differ essen-

tially from those to which we are led by the demon-

strations of pure mathematics, which not only com-

mand our assent to the theorems they establish,

but satisfy us that the contrary suppositions are

absurd.

These examples may suffice to convey a general

idea of the distinction between demonstrative and

probable evidence ; and I purposely borrowed them

from sciences where the two are brought into im-

mediate contrast with each other, and where the

authority of both has hitherto been equally undis-

. puted.

Before prosecuting any farther the subject of pro-

bable evidence, some attention seems to be due, in

the first place, to the grounds of that fundamental


supposition on which it proceeds,

—

the stabiliti/ of

the order ofnature. Of this important subject, ac-

cordingly, I propose to treat at some length.

11.

Conthiiiation of the Subject.—Of that Permanence

or Stability in the Order of Nature, which is

presupposed in our Reasonings coficerning Con-

tingent Truths.

I HAVE ah'eady taken notice of a remarkable

principle of the mind (whether coeval with the first

exercise of its powers, or the gradual result of habit,

it is not at present material to inquire), in conse-

quence of which, we are irresistibly led to apply to

future events the results of our past ex}>erience.

In again resuming the subject, I do not mean to add

anything to what was then stated concerning the

origin or the nature of this principle ; but shall con-

fine myself to a few reflections on that established

order in the succession of events, which it uncon-

sciously assumes as a fact ; and which, if it were not

real, woul^ render human life a continued series of

errors and disappointments. In any incidental re-

marks that m?.y occur on the principle itself, I shall

consider its existence as a thing universally acknow-

ledged, and shall direct my attention chiefly to its

practical effects ;—effects which will be found to ex-

tend equally to the theories of the learned, and to

the prejudices of the vulgar. The question with re-

gard to its origin is, in truth, a problem of mere

curiosity ; for oi" its actual influence on our belief.

Sect. 4- • OF THE HUMAN MIND. 221

and on our conduct, no doubts have been suggested

by the most sceptical writers.

Before entering, however, upon the following

argument, it may not be superfluous to observe, with

respect to this expectation, that, in whatever man-

ner it at first arises, it cannot fail to be mightily con-

firmed and strengthened by habits of scientific re-

search ; the tendency of which is to familiarize us

more and more with the simplicity and uniformity

of physical laws, by gradually reconciling with them,

as our knowledge extends, those phenomena which

we had previously been disposed to consider in the

light of exceptions. It is thus that, when due

allowances are made for the different circumstances

of the two events, the ascent of smoke appears to be

no less a proof of the law of gravitation than the

fall of a stone. This simplification and generali-

zation of the laws of nature is one of the greatest

pleasures which philosophy yields ; and the growing

confidence with which it is anticipated, forms one

of the chief incentives to philosophical pursuits. Fewexperiments, perhaps, in physics afford more ex-

quisite delight to the novice, or throw a stronger

light on the nature and object of that science, than

when he sees, for the first time, the guinea and the

feather drop together in the exhausted receiver.

In the language of modern science, the establish-

ed order m the succession of physical events is com-

monly referred (by a sort of figure or metaphor) to

the general laws of nature. It is a mode of speak-

ing extremely convenient from its conciseness, but

is apt to suggest to the fancy a groundless, and, in-

SS^ ELEMENTS OF THE PHILOSOPHY Chap. If.

deed, absurd analogy between the material and the

moral worlds. As the order of society results from

the lazes prescribed by the legislator, so the order

of the universe is conceived to result from certain

laws established by the Deity. Thus, it is custom-

ary to say, that the fall of heavy bodies towards

the earth's surflice, the ebbing and flowing of the

sea, and the motions of the planets in their orbits,

are consequences of the law of gravitation. But

although, in one sense, this may be abundantly ac-

curate, it ought always to be kept in view, that it is

not a literal, but a metaphorical statement of the

truth ; a statement somewhat analogous to that

poetical expression in the sacred writings, in which

God is said " to have given his decree to the seas,

" that they should not pass his commandment.'*

In those political associations from which the me-

taphor is borrowed, the laws are addressed to ration-

al and voluntary agents, who are able to compre-

hend their meaning, and to regulate their conduct

accordingly ; whereas, in the material universe, the

subjects of our observation are understood by all men

to be unconscious and passive (that is, are under-

stood to be unchangeable in their state, without the

influence of some foreign and external force), and,

consequently, the 07^der so admirably maintained,

amidst all the various changes which they actually

undergo, not only implies intelligence in its first con-

ception, but implies, in its continued existence, the

incessant agency of poxver, executing the purposes

of wise design. If the word lazv, therefore, be, in

such instances, literally intei-preted, it must mean n


uniform mode of operation, prescribed by the Deity

to himself; and it has accordingly been explained

in this sense by some of our best philosophical

writers, particularly by Dr Clarke. * In employ-

ing, however, the word with an exclusive reference

to experimental philosophy, it is more correctly logi-

cal to consider it as merely a statement of some ge^

neral fact with respect to the order of nature ;—

a

fact which has been found to hold uniformly in our

past experience, and on the continuance of which,

in future, the constitution of our mind determines

us confidently to rely.

After what has been already said, it is hardly

necessary to take notice of the absurdity of that

opinion, or rather of that mode of speaking, which

seems to refer the order of the universe to general

laws operating as efficient causes. Absurd, however,

as it is, there is reason to suspect that it has,

with many, had the effect of keeping the Deity out

of view, while they were studying his works. Toan incautious use of the same very equivocal phrase,

may be traced the bewildering obscurity in the specu-

lations of some eminent French writers, concerning

its metaphysical import. Even the great Montes-

quieu, in the very first chapter of his principal work,

has lost himself in a fruitless attempt to explain its

* So likewise Halley, in his Latin verses prefixed to Newton's

Principia

:

" Fn tibi norma poli, et divae libtamina niolis,

" Computus en Jovis ; el quas, dum primordia rerum*' Pangeret, omniparens leges violare Creator

" Noluit."

224 ELEMENTS OF THE PHILOSOFHY Chap. IL

meaning, when, by a simple statement of the essen-

tial distinction between its literal and its metaphori-

cal acceptations, he might have at once cleared up

the mystery. After telling us that " laws, in their

*' most extensive signification, are the necessary re-

" lations (les rapports necessairesj which arise

" fi'om the nature of things, and that, in this sense,

" all beings have their laws ;—that the Deity has

" his laws ; the material world its laws ; intelligen-

" ces superior to man their laws ; the brutes their

" laws ; man his laws ;"—he proceeds to remark,

*' That the moral world is so far from being so well

*' governed as the material ; for the former, al-

" though it has its laws, which are invariable, does

" not observe these laws so constantly as the latter."

It is evident that this remark derives whatever plau-

sibility it possesses from a play upon words ; from

confounding moral laws with phi/sical ; or, in plain-

er terms, from confounding laws which are addres-

sed by a legislator to intelligent beings, with those

general conclusions concerning the established order

of the universe, to which, when legitimately inferred

from an induction sufficiently extensive, philosophers

have metapliorically applied the title of Laws of

Nature. In the one case, the conformity of the

law with the nature of things, does not at all depend

on its being observed or not, but on the reasonable-

ness and moral obligation of the law. In the other

case, the very definition of the word law supposes

that it applies universally ; insomuch that, if it fail-

ed in one single instance, it would cease to be a law.

It is, therefore, a mere quibble to say, that the laws


of the material world are better observed than those

of the moral ; the meaning of the word laWy in the

two cases to which it is here applied, being so total-

ly different, as to render the comparison or contrast,

in the statement of which it is involved, altogether

illusory and sophistical. Indeed, nothing more is

necessary to strip the proposition of every semblance

of plausibility, but an attention to this verbal ambi-

guity. *

This metaphorical employment of the word law,

to express a general fact, although it does not appear

to have been adopted in the technical phraseology of

ancient philosophy, is not unusual among the classi-

cal writers, when speaking of those physical arrange-

ments, whether on the earth or in the heavens, which

continue to exhibit the same appearance from age to

age.

" Hie segetes, illic veniunt felicius uveb:

" Arborei fetus alibi, atque injussa virescunt

* I do not recollect any instance in the writings of Montes-

quieu, where he has reasoned more vaguely than in this chapter;

and yet I am inclined to believe, that few chapters in the Spirit

of Laws have been more admired. " Montesquieu," says a

French writer, " paroissoit a Thomas le premier des ecrivains,

*' pour la force et I'etendue des idees, pour la multitude, la pro-

*' fondeur, la nouveaute des rapports. II est incroyable (disoit-

" il) tout ce que Montesquieu a fait appergevoir dans ce mot si

** court, le mot Loi."

—

Noveau Diction, Historique, Art, Thomas.

Lyon, 1804.

For some important remarks on the distinction between mo-

ral and physical laws, see Dr Ferguson's Institutes of Moral Phi-

losophy, last edit.

VOL, II. P


" Gratnina. Nonne vides, croceos ut Tmolus odores,

" India mittit ebur, moUes sua thura Sabsei ?

" At Chalybes nudi ferrum, virosaque Pontus

" Castorea, Eliadum palraas Epiros equarum ?

" Continue has leges, ajternaque foedera certis

" Imposuit natura locis."*

The same metaphor occurs in another passage of

the Georgics, where the poet describes the regula-

rity which is exhibited in the economy of the bees

:

" SolcB communes natos, consortia tecta

" Urbis habent, magnisque an,itant sub legik/s dsyum."' i

The following lines from Ovid's account of the

Pythagorean philosophy are still more in point

:

" Et rerum causas, et quid natura docebat ;

" Quid Dcus : Unde nives : qufe fulminis esset origo :

" Jupiter, an venti, discussa nube tonarent:

" Quid quateret terras, qua sidcra lege raearent,

" Et quodcunque latet." +

* ^"irg. I. Georg. 60.

+ Georg. IV. 153;

: Ovid. Met. XV. 68.

I shall only add to these quotations the epigram of Claudian

on the instrument said to be invented by Archimedes for repre-

senting the movements of the heavenly bodies, in which various

expressions occur coinciding remarkably with the scope of the

foregoing observations.

" Jupiter in parvo cum cenieret aethera vitro

*' Risit, et ad snpcros talia dicta dcdit,

*' Hucciiie mortalis progressa poteiifia cureej

'* Jam mens in fraîli liulitur orbe labor.

" Jura Poll, rcrumquefidem, legesque Deorum" Ecce Syracusius transtulit arte senex.

" IncUisus variis famulatur spiiitus astris,

" Et viviim certis motibus urget opus.

" Percurrit propriuni raentitus signifer annum,

'' Et simulata novo Cynthia mense redit.


I have quoted these different passages from an-

cient authors, chiefly as an ilhistration of the strength

and of the similarity of the impression which the

order of nature has made on the minds of reflecting

men, in all ages of the world. Nor is this wonder-

ful : for, were things differently constituted, it would

be impossible for man to derive benefit from experi-

ence ; and the powers of observation and memory

would be subservient only to the gratification of an

idle curiosity. In consequence of those uniform

laws by which the succession of events is actually re-

gulated, every fact collected with respect to the past

is a foundation of sagacity and of skill with respect

to the future ; and, in truth, it is chiefly this appli-

cation of experience to anticipate what is yet to hap-

pen, which forms the intellectual superiority of one

individual above another. The remark holds equal-

ly in all the various pursuits of mankind, whether

speculative or active. As an astronomer is able, by

" Jamque suuna volvens audax indusliia muiKlunj

" Gaudet, et liuniana .Sytlcra mente regit.

" Quid falso insontcin toiiih n Salmonea miror ?

" iEninla naturae parva rrpeita manus."

In the propress of philosophical refinement at Rome, this me-

taphorical application of the word /aw seems to have been attend-

ed with the same consequences which (as I already observed)

have resulted from an incautious use of it among some philoso-

phers of modern Europe. Pliny tells us, that, in his time, these

[consequences extended both to the lettered and to the unletter-

ed multitude. " Pars alia astro suo eventus a?signat, ct nascenr

" di legibus ; semelque in omncs futuros unquam Deo dccrctum,

" in reliquum vero otium datum. Sedere cajpit sententia hasc,

" pariterque et eruditum vulgus et rude in cam cursu vadit."—

PUn. Nat. Hist. Lib. ii.

228 ELEMENTS OF THE PHILOSOPHY Chap II.

reasonings founded on past observations, to predict

those phenomena of the heavens which astonish or

terrify the savage ;—as the chemist, from his previ-

ous familiarity with the changes operated upon bodies

by heat or by mixture, can predict the result of in-

numerable experiments, which to others furnish on-

ly matter of amusement and wonder ;—so a studious

observer of human affairs acquires a prophetic fore-

sight (still more incomprehensible to the multitude)

with respect to the future fortunes of mankind ;—

a

foresight which, if it does not reach, like our antici-

pations in physical science, to particular and definite

events, amply compensates for what it wants in pre-

cision, by the extent and variety of the prospects

which it opens. It is from this apprehended analo-

gy between the future and the past, that historical

knowledge derives the whole of its value ; and were

the analogy completely to fail, the records of former

ages would, in point of utility, rank with the fictions

of poetry. Nor is the case different in the business

of common life. Upon what does the success of men

in their private concerns so essentially depend as on

their ovm prudence ; and what else does this word

mean, than a wise regard, in every step of their con-

duct, to the lessons which experience has taught

them ?*

The departments of the universe, in which we

have an opportunity of seeing this regular order

displayed, are the three following : 1. The pheno-

mena of inanimate matter ; 2. The phenomena of

* " Prudentiam qucdammodo esse divinationem."— Cor«.

Nep. in •cita Attici.


the lower animals ; and, 3. The phenomena exhibit-

ed by the human race.

1. On the first of these heads, I have only to re-

peat what was before remarked. That, in all the phe-

nomena of the material world, the uniformity in the

order of events is conceived by us to be complete

and infallible j insomuch that, to be assured of the

same result upon a repetition of the same experi-

ment, we require only to be satisfied, that both have

been made in circumstances precisely similar. Asingle experiment, accordingly, if conducted with

due attention, is considered, by the most cautious

inquirers, as sufficient to establish a general physical

factJand if, on any occasion, it should be repeated

a second time, for the sake of greater certainty in

the conclusion, it is merely with a view of guarding

against the effects of the accidental concomitants

which may have escaped notice, when the first result

was obtained.

2. The case is nearly similar in the phenomena

exhibited by the brutes ; the various tribes of which

furnish a subject of examination so steady, that the

remarks made on a few individuals may be extended,

with little risk of error, to the whole species. Tothis uniformity in their instincts it is owing, that

man can so easily maintain his empire over them,

arid employ them as agents or instruments for ac-

complishing his purposes ; advantages which would

be wholly lost to him, if the operations of instinct

were as much diversified as those of human reason.

Here, therefore, we may plainly trace a purpose or

design, perfectly analogous to that already remark-

^30 ELEMENTS OF THE PHILOSOPHY Ch:ip. IL

ed, with respect to the laws which regulate the ma-

terial world ; and the difference, in point of exact

uniformity, which distinguishes the two classes of

events, obviously arises from a certain latitude of ac-

tion, which enables the brutes to accommodate them-

selves, in some measure, to their accidental situa-

tions ;—rendering them, in consequence of this

power of accommodation, incomparably more service-

able to our race than they would have been, if alto-

gether subjected, like mere matter, to the influence

of regular and assignable causes. It is, moreover,

extremely worthy of observation, concerning these

two departments of the universe, that the uniformity

in the phenomena of the latter presupposes a corre-

sponding regularity in the phenomena of the former

;

insomuch that, if the established order of the mate-

rial world were to be essentially disturbed (the in-

stincts of the brutes remaining the same), all their

various tribes would inevitably perish. The unifor-

mity of animal instinct, therefore, bears a reference

to the constancy and immutability of physical laws,

not less manifest, than that of the fin of the fish to

the propeities of the water, or of the wing of the

bird to those of the atmosphere.

3. When, from the phenomena of inanimate mat-

ter and those of the loner animals, we turn our at-

tention to the history of our own species, innumer-

able lessons present themselves for the instruction of

all who reflect seriously on the great concerns of hu-

man life. These lessons require, indeed, an uncom-

mon degree of acuteness and good sense to collect

them, and a still more uiicommon degree of caution


to apply them to practice ; not only because it is dif-

ficult to find cases in which the combinations of cir-

cumstances are exactly the same ; but because the

peculiarities of individual character are infinite, and

the real springes of action in our fellow-creatures are

objects only of vague and doubtful conjecture. It

is, however, a curious fact, and one which opens a

wide field of interesting speculation, that, in propor-

tion as we extend our views from particulars to ge-

nerals, and from individuals to communities, human

affairs exhibit, more and more, a steady subject of

philosophical examination, and furnish a greater

number of general conclusions to guide our conjec-

tures concerning future contingencies. To specu-

late concerning the character or talents of the indi-

vidual who shall possess the throne of a particular

kingdom, a hundred years hence, would be absurd

in the extreme : But to indulge imagination in anti-

cipating, at the same distance of time, the condition

and character of any great nation, with whose man-

ners and political situation we are well acquainted

(although even here our conclusions may be widely

erroneous), could not be justly censured as a misap-

plication of our faculties equally vain and irrational

with the former. On this subject, Mr Hume has

made some very ingenious and important remarks in

the beginning of his Essay on the Rise and Progress

of the Arts and Sciences.

The same observation is applicable to all other

cases, in which events depend on a multiplicity of

circumstances. How accidental soever these circum-

stances may appear, and how much soever they may

^32 ELEMENTS OF THE PHILOSOPHY Chap. IL

be placed, when individually considered, beyond the

reach of our calculations, experience shews, that they

are somehow or other mutually adjusted, so as to pro-

duce a certain degree of uniformity in the result

;

and this uniformity is the more complete, the great-

er is the number of circumstances combined. Whatcan appear more uncertain than the proportion be-

tween the sexes among the children of any one fa-

mily ! and yet how wonderfully is the balance pre-

served in the case of a numerous society ! Whatmore precarious than the duration of life in an indi-

vidual ! and yet, in a long list of persons of the same

age, and placed in the same circumstances, the mean

duration of life is found to vary within very narrow

limits. In an extensive district, too, a considerable

degree of regularity may sometimes be traced for a

course of years, in the proportion of births and of

deaths to the number of the whole inhabitants.

Thus, in France, Necker informs us, that '' the

*' number of births is in proportion to that of the

" inhabitants as one to twenty-three and twenty-

" four, in the districts that are not favoured by na-

** ture, nor by moral circumstances : this propor-

*' tion is as one to twenty-five, twenty-five and a

" half, and twenty-six, in the greatest part of

*' France : in cities, as one to twenty-seven, twenty-

*' eight, twenty-nine, and even thirty, according to

*' their extent and their trade." *' Such propor-

" tions,'* he observes, " can only be remarked in

*' districts where there are no settlers nor emigrants;

" but even the differences arising from these,'* the

same author adds, ** and many other causes, ac-


" quire a kind of uniformity, when collectively con-

" sidered, and in the immense extent of so great a

" kingdom." *

It may be worth while to remark, that, on the

principle just stated, all the different institutions for

Assurances are founded. The object at which they

all aim, in common, is, to diminish the number of

accidents to which human life is exposed ; or rather,

to counteract the inconveniencies resulting from the

irregularity of individual events, by the uniformity

of general laws.

The advantages which we derive from such gene-

ral conclusions as we possess concerning the order

of nature, are so great, and our propensity to believe

in its existence is so strong, that, even in cases where

the succession of events appear the most anomalous,

we are apt to suspect the operation of fixed and con-

stant laws, though we may be unable to trace them.

The vulgar, in all countries, perhaps, have a propen-

sity to imagine, that, after a certain number of years,

the succession of plentiful and of scanty harvests be-

gins again to be repeated in the same series as be-

fore ;—a notion to which Lord Bacon himself has

given some countenance in the following passage

:

" There is a toy which I have heard, and I would** not have it given over, but waited upon a little.

" They say it is observed in the Low Countries (I

*' know not in what part), that every five and thirty

" years, the same kind and suite of years and wea-

" thers come about again j as great frosts, great wet,

* Traite de I'Administration des Finances de France.


" great droughts, warm winters, summers with little

" heat, and the like ; and they call it the prime.

«' It is a thing I do the rather mention, because,

" computing backwards, I have found some concur-

" rence." *

Among the philosophers of antiquity, the influ-

ence of the same prejudice is observable on a scale

still greater ; many of them having supposed, that at

the end of the annus 7uagtius, or Platonic year, a

repetition would commence of all the transactions

that have occurred on the theatre of the world. Ac-

cording to this doctrine, the predictions in Virgil's

Pollio will, sooner or later, be literally accomplished

:

*' Alter erit turn Tiphys, et altera quae vehat Argo

" Delectos Heroas ; erunt ctiam altera bella;

" Atque iterum ad Trqjam magnus mittetur Achilles." +

The astronomical cycles which the Greeks bor-

rowed from the Egyptians and Chaldeans, when com-

bined with that natural bias of the mind which I

have just remarked, account sufficiently for this ex-

tension to the moral world, of ideas suggested by the

order of physical phenomena.

* Essays, Art. 59-

+ " Turn cfficitur," says Cicero, speaking of this period, " cum

" solis et lunae, et quinque crranlium ad eandem inter se compa-

" ratiouem confectis omnium spatiis, est facta conversio. Quae

" quam longa sit, magna quaestio est : essevero certamef definitam

" neccsseest"—De Nat. Deorian, Lib. ii. 74. " Hoc intervallo,"

Clavius observes, " quidam volunt, omnia qucecunque in mun-

" do sunt, eodem ordine esse reditura, quo nunc cernuntur."

—

Clav. Commentur. in Sphceram Joannis de Sacro BoscOf p. 57-

Romae, 1607.6

Sect. 4. OF THE HUMAN BIIND. 235

Nor is this hypothesis of a moral cycle^ extrava-

gant as it unquestionably is, without its partisans

among modern theorists. The train of" thouglit, in-

deed, by which they have been led to adopt it is es-

sentially different ; but it probably received no small

degree of countenance, in their opinion, from the

same bias which influenced the speculations of the

ancients. It has been demonstrated by one of the

most profound mathematicians of the present age, *

that all the irregularities arising from the mutual ac-

tion of the planets are, by a combination of various

arrangements, necessarily subjected to certain peri-

odical laws, so as for ever to secure the stability and

order of the system. Of this sublime conclusion it

has been justly and beautifully observed, that " after

" Newton's theory of the elliptic orbits of the pla-

" nets. La Grange's discovery of their periodical in-

*' equalities is, without doubt, the noblest truth in

" physical astronomy ; while, in respect of the doc-

*' trine of final causes, it may truly be regarded a^

'* the greatest of all." t The theorists, however,

to whom I at present allude, seem disposed to con-

sider it in a very different light, and to employ it

for purposes of a very different tendency. *' Simi-

" lar periods (it has been said), but of an extent that

** affright the imagination, probably regulate the

*' modifications of the atmosphere ; inasmuch as the

" same series of appearances must inevitably recur,

" whenever a coincidence of circumstances takes

" place. The aggregate labours of men, indeed,

* M. De la Grange.

+ Efiinburgli Iloviev.-. Vol, XI. p. 2(j4.

2B6 ELEMENTS OF THE PHILOSOPHY Chap. 11.

" may be supposed, at first sight, to alter the opera-

** tion of natural causes, by continually transforming

*' the face of our globe ; but it must be recollected

•* that, as the agency of animals is itself stimulated

" and determined solely by the influence of external

" objects, the re-actions of living beings are compre-

" hended in the same necessary system ; and, con-

" sequently, that all the events within the immea'-

** surable circuit of the universe, are the successive

" evolution of an extended series, which, at the re- '

•* turns of some vast period, repeats its eternal round

" during the endless flux of time." *

On this very bold argument, considered in its

connection with the scheme of necessity, I have no-

thing to observe here. I have mentioned it merely

as an additional proof of that irresistible propensity

to believe in the permanent order of physical events,

which seems to form an original principle of the

human constitution ;—a belief essential to our exist-

ence in the world which we inhabit, as well as the

foundation of all physical science j but which we

obviously extend far beyond the bounds authorized

by sound philosophy, when we apply it, without any

limitation, to that moral system, which is distinguish-

ed by peculiar characteristics, so numerous and im-

portant, and for the accommodation of which so

many reasons entitle us to presume, that the mate-

* The foregoing passage is transcribed from an article in the

Monthly Review. I have neglected to mark the volume j but I

think it is one of those published since 1800.

See Note (I.)

1

Sect. 4.. OF THE HUMAN MIND. 237

rial universe, with all its constant and harmonious

laws, was purposely arranged.

To a hasty and injudicious application of the same

belief, in anticipating the future course of human

affairs, might be traced a variety of popular super-

stitions, which have prevailed, in a greater or less

degree, in all nations and ages ; those superstitions,

for example, which have given rise to the study of

charms, of omens, of astrology, and of the different

arts of divination. But the argument has been al-

ready prosecuted as far as its connection with this

part of the subject requires. For a fuller illustra-

tion of it, I refer to some remarks in my former vo-

lume, on the superstitious observances which, among

rude nations, are constantly found blended with the

practice of physic ; and which, contemptible and lu-

dicrous as they seem, have an obvious foundation,

during the infancy of human reason, in those im-

portant principles of our nature, which, when duly

disciplined by a more enlarged experience, lead to

the sublime discoveries of inductive science. *

Nor is it to the earlier stages of society, or to the

lower classes of the people, that these superstitions

are confined. Even in the most enlightened and

refined periods they occasionally appear ; exercising

not unfrequently, over men of the highest genius

and talents, an ascendant, which is at once consola-

tory and humiliating to the species.

** Ecce fulgurum monitus, oraculorum praescita,

** aruspicum prêdicta, atque etiam parva dictu in

* Vol. I. pp. 355, 356, 357, 3d edit.

S38 ELEMENTS OF THE PHILOSOPHY Chap. II.

" auguriis sternutamenta et offensiones pedum.

" Divus Augustus lasvum prodidit sibi calceum prae-

" postere inductum, quo die seditione militari prope

" afflictus est." *

" Dr Johnson,'* says his affectionate and very com-

municative biographer, " had another particularity,

" of which none of his friends ever ventured to ask

*' an explanation. It appeared to me some super-

" stitious habit, which he had contracted early, and

" from which he had never called upon his reason

" to disentangle him. This was, his anxious care

" to go out or in at a door or passage, by a certain

" number of steps from a certain point, or at least so

" as that either his right or his left foot (I am not

" certain which) should constantly make the first

" actual movement when he came close to the door

** or passage. Thus I conjecture : for I have, upon

*' innumerable occasions, observed him suddenly

" stop, and then seem to count his steps with a

" deep earnestness ; and when he had neglected or

*' gone wrong in this sort of magical movement, I

*' have seen him go back again, put himself in a

" proper posture to begin the ceremony, and, hav-

" ing gone through it, break from his abstraction,

" walk briskly on, and join his companion.'* t

The remark may appear somewhat out of place,

but, after the last quotation, I may be permitted to

say, that the person to whom it relates, great as

his powers, and splendid as his accomplishments un-

doubtedly were, was scarcely entitled to assert, that

* Plin. Nat. Hist. Lib. ii.

+ Boswcll's Johnson, Vol. I. p. 26-t, 4to edit.


" Education is as well known, and has long been as

" well known, as ever it can be." * What a limit-

ed estimate of the objects of education must this

great man have formed ! They who know the va-

lue of a well regulated and unclouded mind, would

not incur the weakness and wretchedness exhibited

in the foregoing description, for all his literary ac-

quirements and literary fame.

III.

Conti?mation of the Subject.—General Remarks on

the Difference between the Evidence ofEa^peri-

ence and that of Analogy.

According to the account of experience which

has been hitherto given, its evidence reaches no far-

ther than to an anticipation of the future from the

past, in cases where the same physical cause con-

tinues to operate in exactly the same circumstances.

That this statement is agreeable to the strict philo-

sophical notion of experience, will not be disputed.

Wberever a change takes place, either in the cause

itself, or in the circumstances combined with it in

our former trials, the anticipations which we form of

the future cannot with propriety be referred to ex-

perience alone, but to experience co-operating with

some other principles of our nature. In common

discourse, however, precision in the use of language

is not to be expected, where logical or metaphysical

ideas are at all concerned ; and, therefore, it is not

* Boswell's Johnson, Vol. I. p. 514, 4to edit.


to be wondered at, that the word experience should

often be employed with a latitude greatly beyond

what the former definition authorizes. When I

transfer, for example, my conclusions concerning

the descent of heavy bodies from one stone to an-

other stone, or even from a stone to a leaden bullet,

my inference might be said, with sufficient accuracy

for the ordinary purposes of speech, to have the evi-

dence of experience in its favour; if, indeed, it would

not savour of scholastic affectation to aim at a more

rigorous enunciation of the proposition. Nothing,

at the same time, can be more evident than this, that

the slightest shade of difference which tends to

weaken the resemblance, or rather to destroy the

identity of two cases, invalidates the inference from

the one to the other, as far as it rests on experience

solely, no less than the most prominent dissimili-

tudes which characterize the different kingdoms and

departments of nature.

Upon what ground do I conclude that the thrust

of a sword through my body, in a particular direc-

tion, would be followed by instant death ? Accord-

ing to the popular use of language, the obvious an?

swer would be,—upon experience, and experience

alone. But surely this account of the matter is ex-

tremely loose and incorrect ; for where is the evi-

dence that the internal structure of my body bears

any resemblance to that of any of the other bodies

which have been hitherto examined by anatomists ?

It is no answer to this question to tell me, that the

experience of these anatomists has ascertained a uni-

formity of structure in every human subject which


has as yet been dissected ; and that, therefore, I amjustified in concluding, that my body fonns no ex-

ception to the general rule. My question does not

relate to the soundness of this inference, but to the

principle of my nature, which leads me thus not

only to reason from, the past to the future, but to

reason from one thing to another, which, in its ex-

ternal marks, bears a certain degree of resemblance

to it. Something more than experience, in the

strictest sense of that word, is surely necessary to

explain jthe transition from what is identically the

same, to what is only similar ; and yet my inference

in this instance is made with the most assured and

unqualified confidence in the infallibility of the re-

sult. No inference, founded on the most direct and

long-continued experience, nor, indeed, any proposi-

tion established by mathematical demonstration,

could more imperiously command my assent.

In whatever manner the province of experience,

strictly so called, comes to be thus enlarged, it is

perfectly manifest, that, without some provision for

this purpose, the principles of our constitution would

not have been duly adjusted to the scene in which

we have to act. Were we not so formed as eagerly

to seize the resembling features of different things

and different events, and to extend our conclusions

from the individual to the species, life would elapse

before we had acquired the first rudiments of that

knowledge which is essential to the presei-vation of

our animal existence.

This step in the history of the human mind has

VOL. II, Q

242 ELEBIENTS OF THE PHILOSOPHY Chap. IF.

been little, if at all, attended to by philosophers;

and it is certainly not easy to explain, in a manner

completely satisfactory, how it is made. The follow-

ing hints seem to me to go a considerable way to-

wards a solution of the difficulty.

It is remarked by Mr Smith, in his Considerations

on the Formation of Languages, that the origin of

genera and species, which is commonly repi'esented

in the schools as the effect of an intellectual pro-

cess peculiarly mysterious and unintelligible, is a na-

tural consequence of our disposition to transfer to a

new object the name of any other familiar object,

which possesses such a degree of resemblance to it,

as to serve the memory for an associating tie between

them. It is in this manner, he has shewn, and not

by any formal or scientific exercise of abstraction,

that, in the infancy of language, proper names are

gradually transformed into appellatives ; or, in other

words, that individual things come to be referred to

classes or assortments. *

This remark becomes, in my opinion, much more

luminous and important, by being combined with

* A writer of'great learning and ability (Dr Magce of Dublin),

who has done me the honour to animadvert on a few passages of

my works, and who has softened his criticisms by sonle ex-

pressions of regard, by which I feel myself highly flattered, has

started a very acute objection to this theory of INIr Smith, which

I think it incumbent on me to submit to my readers, in his own

words. As the quotation, however, with the remarks which I

have to offer upon it, would extend to too great a length to be

introduced here, I must delay entering on the subject till the end

of this volume. See Note (K.)

S«ct. 4. OF THE HUMAN MIND. 243

another very original one, which is ascribed to Tur-

got by Condorcet, and which I do not recollect to

have seen taken notice of by any later writer on the

human mind. According to the common doctrine

of logicians, we are led to suppose that our know-

ledge begins in an accurate and minute acquaint-

ance with the characteristical properties of indivi-

dual objects ; and that it is only by the slow exer-

cise of comparison and abstraction, that we attain to

the notion of classes or genera. In opposition to

this idea, it was a maxim of Turgot's, that some of

our most abstract and general notions are among; the

earliest which we form. * What meaning he an-

nexed to this maxim, we are not informed ; but if

he understood it in the same sense in which I amdisposed to interpret it, he appears to me entitled to

the credit of a very valuable suggestion with respect

to the natural progress of human knowledge. The

truth is, that our first perceptions lead us invariably

*" M. Turgot croyoitqu'on s'etoit trompe en imaginant qu'en

" general I'esprit n'acquiert des idAes generalesou abstraites que

" par la comparaison d'idees plus particuli^res. Au contraire,

" nos premieres idees sont tres-generales, puisque ne voyant

" d'abord qu'un petit nombre do qualites, uotre idee renferme-

*^ tous les etres auxquels ces qualites sont communes. En nous

" eclairant, en examinant davantage, nos idees deviennent plus

" particuliercs sans jamais atteindre le dernier terme; et ce qui

" a pu tromper les m^taphysiciens, c'est qu'alors precisement

" nous apprenons que ces idees sont plus generales que nous ne

" I'avions d'abord suppose."—F/e dt Turgot^ p. 189. Berne,

1787.

I have searched in vain for some additional light on this inte-

resting hint, in the complete edition of Turgot's works, published

at Paris in 1 808,

^24>4f ELEMENTS OP THE PHILOSOPHY Chap. II.

to confound together things wliich have very little in

common ; and that the specifical differences of indi-

viduals do not begin to be marked with precision

till the powers of observation and reasoning have

attained to a certain degree of maturity. To a si-

milar indistinctness of perception are to be ascribed

the mistakes about the most familiar appearances

which we daily see committed by those domesticat-

ed animals, with whose instincts and habits we have

an opportunity of becoming intimately acquainted.

As an instance of this, it is sufficient to mention the

terror which a horse sometimes discovers in passing,

on the road, a large stone, or the waterfall of a mill.

Notwithstanding, however, the justness of this

maxim, it is nevertheless true, that every scientific

classification must be founded on an examination

and comparison of individuals. These individuals

must, in the first instance, have been observed with

accuracy, before their specific characteristics could be

rejected from tlie generic description, so as to limit

tlie attention to the common qualities which it com-

prehends. What are usually called general ideas

on: general noimiSy are, therefore, of two kinds, essen-

tially different from each other ; those which are

gc?ietril, merely from the vagueness and imperfec-

tion of our information ; and tliose which have been

methodically generalized^ in the way explained by

logicians, in consequence of an abstraction founded

on a careful study of particulars. Philosophical

precision requires, that two sets of notions, so total-

ly dissimilar, should not be confounded together

;

and an attention to the distinction between them12

Sect. 4. O^ "^^^ HUMAN MIND. 245

will be found to throw much light on various im-

portant steps in the natural history of the mind. *

One obvious effect of the grossness and vagueness

in the perceptions of the inexperienced observer,

must necessarily be to identify, under the same com-

mon appellations, immense multitudes of individuals,

which the philosopher will afterwards find reason to

distinguish carefully from each other ; and as lan-

guage, by its unavoidable reaction on thought, never

fails to restore to it whatever imperfections it has

once received, all the indistinctness which, in the

case of individual observers, originated in an ilLin-

foraied judgment, or in a capricious flmcy, comes

afterwards, in succeeding ages, to be entailed on the

* The distinction above stated furnishes what seems to mc the

true answer to an argument which Charron, antl many other

writers since his time, have drawn, in proof of the reasoning

powers of brutes, from the universal conclusions which they ap-

pear to i'ound on the observation of particulars. " Les bestes

" des singuliers concluent les universels, du regard d'un homme" scul cognoissent tous hommes," &c. &c.

—

De la Sagcsse, Lib. I.

Chap. 8.

Instead of saying, that brutes generalize things which are simi-

lar, would it not be nearer the truth to say, that- they confound

things which are different ?

Many years after these observations were written, I had the sa-

tisfaction to meet with the following experimental confirmation

of them, in the Abbe Sicard's Course of Instruction for the Deaf

and Dumb :" J'avois remarque que Massieu donnoit plus vo-

" lontiers le meme nom, un nom commun, a plusieurs individus

" dans lesquels il trouvoit des traits de ressemblance ; les noms in-

" dividuels supposoient des differences qu'il n'etoit pas encore

" temps de lui faire observer." (Sicardy pp. 30, 31.) The whole

of the passage is well worth consulting.

^46 ELEMENTS OF THE PHILOSOPHY Chap. 11.

infant understanding, in consequence of its incoi'po-

ration with vernacular speech. These confused ap-

prehensions produced by language, must, it is easy

to see, operate exactly in the same way as the un-

distinguishing perceptions of children or savages ;

the familiar use of a generic word, insensibly and ir-

resistibly leading the mind to extend its conclusions

from the individual to the genus, and thus laying

the foundation of conclusions and anticipations which

we suppose to rest on experience, when, in truth,

experience has never been consulted.

In all such instances, it is worthy of observation,

we proceed ultimately on the common principle,

—

that in similar circumstances, the same cause will

produce the same effects ; and, when we err, the

source of our error lies merely in identifying differ-

ent cases which ought to be distinguished from each

other. Great as may be the occasional inconve-

niences, arising from this general principle thus

misapplied, they bear no proportion to the essential

advantages resulting from the disposition in which

they originate, to arrange and to classify ; a dispo-

sition on which (as I have elsewhere shewn) the

intellectual improvement of the species in a great

manner hinges. That the constitution of our na-

ture in this respect is, on the whole, wisely ordered,

as well as perfectly conformable to the general eco-

nomy of our frame, will appear from a slight survey

of some other principles, nearly allied to those which

are at present under our consideration.

It has been remarked by some eminent writers in

10

Sect. 4. OF THE HUMAN MIND. ^4^7

this part of the island, * that our expectation of the

continuance of the laws of nature has a very close

affinity to our faith in human testimony. The pa-

rallel might perhaps be carried, without any over-

refinement, a little farther than these writers have

attempted ; inasmuch as, in both cases, the instinc-

tive principle is in the first instance unlimited, and

requires, for its correction and regulation, the les-

sons of subsequent ex}>erience. As the credulity of

children is originally without bounds, and is after-

wards gradually checked by the examples which they

occasionally meet with of human falsehood, so, in

the infancy of our knowledge, whatever objects or

events present to our senses a strong resemblance to

each other, dispose us, without any very accurate

examination of the minute details by which they

may be really discriminated, to conclude with eager-

ness, that the experiments and observations which

we make with respect to one individual, may be

safely extended to the whole class. It is experience

alone that teaches us caution in such inferences, and

subjects the natural principle to the discipline pre-

scribed by the rules of induction.

It must not, however, be imagined, that, in in-

stances of this sort, the instinctive principle always

leads us astray ; for the analogical anticipations

which it disposes us to form, although they may

not stand the test of a rigorous examination, may

yet be sufficiently just for all the common purposes

* See Reid's Inquiry into the Human Mind, Criap. \i. Sect.

24. Campbell's Dissertation on Miracles, Part I. Sect. 1 . Smith's

Theory of Moral Sentiments, Vol. II. p. 382, sixth edition.


of life. It is natural, for example, that a man who

has been educated in Europe should expect, when

he changes his residence to any of the other quar-

ters of the globe, to see heavy bodies fall down-

wards, and smoke to ascend, agreeably to the gene-

ral laws to which he has been accustomed ; and that

he should take for granted, in providing the means

of his subsistence, that the animals and vegetables

which he has found to be salutary and nutritious in

his native regions, possess the same qualities wher-

ever they exhibit the same appearances. Nor are

such expectations less useful than natural ; for they

are completely realized, as far as they minister to

the gratification of our more urgent wants. It is

only when we begin to indulge our curiosity with

respect to those nicer details which derive their in-

terest from great refinement in the arts, or from a

very advanced state of physical knowledge, that we

discover our first conclusions, however just in the

main, not to be mathematically exact ; and are led

by those habits which scientific pursuits communi-

cate, to investigate the difference of circumstances

to which the variety in the result is owing. After

having found that heavy bodies fall downwards at

the equator as they do in this island, the most ob-

vious, and perhaps, on a superficial view of the

question, the most reasonable inference would be,

that the same pendulum which swings seconds at

London, will vibrate at the same rate under the

line. In this instance, however, the theoretical in-

ference is contradicted by the fact ;—but the con-

tradiction is attended with no practical inconve-


nieiice to the multitude, while, in the mind of the

philosopher, it only serves to awaken his attention

to the different circumstances of the two cases, and,

in the last result, throws a new lustre on the sim-

plicity and uniformity of that law, from which it

seemed, at first sight, an anomalous deviation.

To this uniformity in the laws which regulate the

order of physical events, there is something ex-

tremely similar in the systematical regularity (sub-

ject, indeed, to many exceptions) which, in every

language, however imperfect, runs through the dif-

ferent classes of its words, in respect of their in-

flexions, forms of derivation, and other verbal filia-

tions or affinities. How much this regularity or

analogy (as it is called by grammarians) contri-

butes to facilitate the acquisition of dead and foreign

languages, every person, who has received a liberal

education, knows from his own experience. Nor is

it less manifest, that the same circumstance must

contribute powerfully to aid the memories of chil-

dren in learning to speak their mother-tongue. It

is not my present business to trace the principles in

the human mind by which it is produced. All that

I would remark is, the very early period at which it

is seized by children ; as is strongly evinced by their

disposition to push it a great deal too far, in their

first attempts towards speech. This disposition seems

to be closely connected with that which leads them

to repose faith in testimony ; and it also bears a

striking resemblance to that which prompts them to

extend their past experience to those objects and

events of which they have not hitherto had any


means of acquiring a direct knowledge. It is pro-

bable, indeed, that our expectation, in all these cases,

has its origin in the same common prmciples of our

nature ; and it is tertain that, in all of them, it is

subservient to the important purpose of facilitating

the progress of the mind. Of this nobody can

doubt, who considers for a moment, that the great

end to be first accomplished was manifestly the

communication of the general rule ; the acquisition

of the exceptions (a knowledge of which is but of

secondary importance) being safely entrusted to the

growing diligence and capacity of the learner.

The considerations now stated may help us to

conceive in what manner conclusions derived from

experience come to be insensibly extended from the

individual to the species;

partly in consequence of

the gross and undistinguishing nature of our first

perceptions, and partly in consequence of the magi-

cal influence of a common name. They seem also

to shew, that this natural process of thought, though

not always justified by n sound logic, is not without

its use in the infancy of human knowledge.

In the various cases which have been hitherto

under our review, our conclusions are said in popu-

lar, and even in philosophical language, to be found-

ed on experience. And yet the truth unquestion-

ably is (as was formerly observed), that the evi-

dence of experience reaches no farther than to an

anticipation of the future from the past, in instances

where the same cause continues to operate in cir-

cumstances exactly similar. How much this vague-

Sect. 4. OV THE HUMAN MIND. S51

ness of expression must contribute to mislead us in

many of our judgments will afterwards appear.

The observations which I have to offer upon ana-

logy, considered as a ground of scientific conjecture

and reasoning, will be introduced with more pro-

priety in a future chapter.

IV.

Continuation of the Subject.—Evidence of Testi-

mony tacitly recognised as a Ground of Belief

in our most certain Conclusions concerning Con-

tinge?it Truths.—Difference between the Logical

and the Popular Meaning of the word Proba-

bility,

In some of the conclusions which have been al-

ready under our consideration with respect to con-

tingent truths, a species of evidence is admitted, of

which no mention has hitherto been made ; I mean

the evidence of testimony. In astronomical calcu-

lations, for example, how few are the instances in

which the data rest on the evidence of our own

senses ; and yet our confidence in the result is not,

on that account, in the smallest degree weakened.

On the contrary, what certainty can be more com-

plete, than that with which we look forward to an

eclipse of the sun or the moon, on the faith of ele-

ments and of computations which we have never

verified, and for the accuracy of which we have no

ground of assurance whatever, but the scientific re-

putation of the writers from whom we have borrow-

ed them ? An astronomer who should affect any


scepticism with respect to an event so predicted,

would render himself no less an object of ridicule,

than if he were disposed to cavil about the certainty

of the sun's rising to-morrow.

Even in pure mathematics, a similar regard to

testimony, accompanied with a similar faith in the

faculties of others, is by no means uncommon. Whowould scruple, in a geometrical investigation, to

adopt, as a link in the chain, a theorem of Appollo-

nius or of Archimedes, although he might not have

leisure at the moment to satisfy himself, by an ac-

tual examination of their demonstrations, that they

had been guilty of no paralogism, either from acci-

dent or design, in the course of their reasonings ?

In our anticipations of astronomical phenomena,

as well as in those which we form concerning the re-

sult of any familiar experiment in physics, philoso-

phers are accustomed to speak of the event as only

probable ; although our confidence in its happen-

ing is not less complete, than if it rested on the ba-

sis of mathematical demonstration. The word pro-

bable, therefore, when thus used, does not imply any

deficiency in the proof, but only marks the particu-

lar nature of that proof, as contradistinguished from

another species of evidence. It is opposed, not to

what is certain^ but to what admits of being demon-

strated after the manner ofmathematicians. This

differs widely from the meaning annexed to the same

word in popular discourse ; according to which,

whatever event is said to be probable^ is understood

to be expected with some degree of doubt. As cer-

tain as death

y

—as cet^tain as the rising ofthe sun,'-^

Sect. 4. OF THE HUMAN MIND. <i5S

are proverbial modes of expression in all countries ;

and they are, both of them, borrowed from events

which, in philosophical language, are only probable

or contingent. In like manner, the existence of

the city of Pekin, and the reality of Caesar's assassi-

nation, which the philosopher classes with probabili-

ties, because they rest solely upon the evidence of

testimony, are universally classed with certainties by

the rest of mankind ; and in any case but the state-

ment of a logical theoiy, the application to such

truths of the word probable would be justly regard-

ed as an impropriety of speech. This difference be-

tween the technical meaning of the word probabi-

lity, as employed by logicians, and the notion usual-

ly attached to it in the business of life ; together

with the erroneous theories concerning the nature

of demonstration, which I have already endeavoured

to refute,—have led many authors of' the highest

name, in some of the most important arguments

which can employ human reason, to overlook that

irresistible evidence which was placed before their

eyes, in search of another mode of proof altogether

unattainable in moral inquiries, and which, if it could

be attained, would not be less liable to the cavils of

sceptics.

But although, in philosophical language, the epi-

thet probable be applied to events which are acknow-

ledged to be certain, it is also applied to those events

which are called probable by the vulgar. The phi-

losophical meaning of the word, therefore, is more

comprehensive than the popular ; the former denot-


ing that particular species of evidence of which con-

tingent truths admit ; the latter being confined to

such degrees of this evidence as fall short of the

highest. These different degrees of probabiliti/ the

philosopher considers as a seties, beginning with

bare possibility, and terminating in that apprehend-

ed infalUhiUty, with which the phrase moral certain-

ty is synonymous. To this last term of i\\e series

the word probable is, in its ordinary acceptation,

plainly inapplicable.

The satisfiiction which the astronomer derives

from the exact coincidence, in point of time, be-

tween his theoretical predictions concerning the phe-

nomena of the heavens, and the corresponding events

when they actually occur, does not imply the smal-

lest doubt, on his part, of the constancy of the laws

of nature. It resolves partly into the pleasure of ar-

rivino; at the knowledo-e of the same truth, or of the

same fact, by different media ; but, chiefly, into the

gratifying assurance which he thus receives of the

correctness of his principles, and of the competency

of the human faculties to these sublime investiga-

tions. ^\'liat exquisite delight must La Place have

felt, when, by deducing from the theory of gravita-

tion, the cause of the acceleration of the moon*s

mean motion,—an acceleration which proceeds at the

rate of little more than 11'' in a century,—he ac-

counted, with such mathematical precision, for all

the recorded observations of her place from the in-

fancy of astronomical science ! It is from the length

and abstruseness, however, of the reasoning process.

Sect. 4. OF THE HUMAN MIND. Q55

and from the powerful effect produced on the miagi-

nation, by a calculus which brings into immediate

contrast with the immensity of time, sucli evanes-

cent elements as tlie fractional parts of a second,

that the coincidence between tlie computation and the

event appears in this instance so peculiarly striking.

In other respects, our confidence in the future result

rests on the same principle with our expectation that

the sun will rise to-morrow at a particular instant;

and, accordingly, now that the correctness of the

theory has been so wonderfully verified by a compa-

rison with facts, the one event is expected with no

less assurance than the other.

With respect to those inferior degrees o^probabi-

lity to which, in common discourse, the meaning of

that word is exclusively confined, it is not my inten-

tion to enter into any discussions. The subject is

of so great extent, that I could not hope to throw

upon it any lights satisfactory either to my reader or

to myself, without encroaching upon the space des-

tined for inquiries more intimately connected with

the theory of our reasoning powers. One set of

questions, too, arising out of it (I mean those to

which mathematical calculations have been applied

by the ingenuity of the moderns), involve some

veiy puzzling metaphysical difficulties, * the consi-

deration of which would completely interrupt the

train of our present speculations. I proceed, there-

* I allude more particularly to the doubts started on this sub-

ject by D'Alembert, in his Opuscules Mathematiciues ; and in

his Melanges de Litlerature.


fore, in continuation of those in which we have been

lately engaged, to treat of other topics of a more ge-

neral nature, tending to illustrate the logical proce-

dure of the mind in the discovery of scientific truth.

As an introduction to these, I propose to devote one

whole chapter to some miscellaneous strictures and

reflections on the logic of the schools.

Sect. 1. OF THE HUMA>^ MIND. S57

CHAPTER THIRD.

OF THE ARISTOTELIAN LOGIC.

Section I.

Ofthe Demonstratio7is ofthe Sijllogistk RuleS given

by Aristotle and his Commeîtators,

1 HE great variety of speculations which, in the pre-

sent state of science, the Aristotelian logic natural-

ly suggests to a philosophical inquirer, lays me, in

this chapter, under the necessity of selecting a few

leading questions, bearing immediately upon the par-

ticular objects which I have in view. In treating

of these, I must, of course, suppose my readers to

possess some previous acquaintance with the subject

to which they relate ; but it is only such a general

knowledge of its outlines and phraseology, as, in all

universities, is justly considered as an essential ac-

complishment to those who receive a liberal educa-

tion.

I begin with examining the pretensions of the

Aristotelian logic to that pre-eminent rank which

it claims among the sciencesj

professing, not only

vol. II. II

g58 ELEMENTS OF THE PHILOSOPHY Chap. IIP.

to rest all its conclusions on the inniioveable basis of

demonstration, but to have reared this mighty fabric

on the narrow ground-work of a single axiom. " On" the basis/* says the latest of his commentators,

" of one simple truth, Aristotle has reared a lofty

" and various structure of abstract science, clearly

" expressed and fully demonstrated." * Nor have

these claims been disputed by mathematicians them-

selves. " In logica," says Dr Wallis, *' structura

" syllogismi demonstratione nititur pure^mathemati-

" ca." t And, in another passage : " Sequitur in-

" stitutio logica, communi usui accommodata.—Quo*' videant Tirones, syllogismorum leges strictissimis

" demonstrationibus plane mathematicis ita fundatas,

" ut consequentias habeant irrefragabiles, quaeque

" offuciis fallaciisque detegendis sint accommoda-

*' ta?." t Dr Reid, too, although he cannot be just-

ly charged, on the whole, with any undue reverence

for the authority of Aristotle, has yet, upon one oc-

casion, spoken of his demonstrations with much more

respect than they appear to me entitled to. "I be-

*' lieve," says he, " it will be difficult, in any

" science, to find so large a system of truths of so

" very abstract and so general a nature, all fortified

" by demonstration, and all invented and perfected

" by one man. It shews a force of genius, and la-

* Analysis of Aristotle'.-, Works by Dr Gillies, Vol. I. p. S3,

2d edit.

+ See the Monitum prefixed to the Miscellaneous Treatises

annexed to the third Volume of Di Wallis's Mathematical

Works.

X Preface to the same volume.


" bour of investigation, equal to the most arduous

" attempts."*

As the fact which is so confidently assumed in

these passages would, if admitted, completely over-

turn all I have hitherto said concerning the nature

both of axioms and of demonstrative evidence, the

observations which follow seem to form a necessary

sequel to some of the preceding discussions. I ac-

knowledge, at the same time, that my chief motive

for introducing them, was a wish to counteract the

effect of those triumphant panegyrics upon Aristo-

tle's Organon, which of late have been pronounced

by some writers, whose talents and learning justly

add much weight to their literary opinions^; and an

anxiety to guard the rising generation against a

waste of time and attention, upon a study so little

fitted, in my judgment, to reward their labour.

The first remark which I have to offer upon

Aristotle's demonstrations, is, That they proceed on

the ob\iously false supposition of its being possible

to add to the conclusiveness and authority of demon-

strative evidence. One of the most remarkable cir-

cumstances which distinguishes this from that species

of evidence which is commonly called moral or pro-

* Analysis of Aristotle's Logic.

That Dr Rcid, however, was perfectly aware that these demon-strations are more specious than solid, may be safely inferred

from a sentence which afterwards occurs in the same tract.

" When we go without the circle of the mathematical sciences, I

" know nothing in which there seems to be so much demonstra-" tion as in that part of logic which treats of the figures and" modes of syllogisms."

260 ELEMENTS OF THE PHILOSOPHY Chap. III.

bable is, tliat it is not susceptible of degrees ; the

process of reasoning, of whicli it is the result, being

eitlier good for nothing, or so perfect and complete

in itself, as not to admit of support from any adven-

titious aid. Every such process of reasoning, it is

well known, may be resolved into a series of legiti-

mate syllogisms, exhibiting separately and distinctly,

in a light as clear and strong as language can afford,

each successive link of the demonstration. How far

this conduces to render the demonstration more con-

vincing than it was before, is not now the question.

Some doubts may reasonably be entertained upon

this head, when it is considered, that, among the va-

rious expedients employed by mathematical teachers

to assist the apprehension of their pupils, none of

them have ever thought of resolving a demonstration

(as may always be easily done) into the syllogisms

of which it is composed. * But, abstracting alto-

* From a passage, indeed, in a memoir by Leibnitz (printed

in the sixth volume of the Acta Eruditorum), it would seem, that

a commentary of this kind, on the first six books of Euclid, hail

been actually carried into execution by two writers, whose names

he mentions. " Firma autem demonstratio est, quae praescrip-

" tam a logica formam servat, non quasi semper ordinatis schola-

" rum more syllogismis opus sit (quales Christianus Herlinus et

" Conradns Dasypodius in sex priores Euclidis libros exhibuerunt)

" sed ita saltern ut argumcntatio concludat vi formte," &c. &c.

Acta Eruditur. Lips. Vol. I. p. 285. Venet. 1740.

I have not seen either of the works alluded to in the above

sentence ; and, upon less respectable authority, should scarcely

have conceived it to be credible, that any person, capable of un-

derstanding Euclid, had ever seriously engaged in such an un-

dertaking. It would have been difiicult to devise a more effectual

12

Sect. 1, OF THE HUMAN Mmo. 261

gether from this consideration, and granting that a

demonstration may be rendered more manifest and

satisfactory by being syllogistically stated ; upon

what principle can it be supposed possible, after the

demonstration has been thus analysed and expanded,

to enforce and corroborate, by any subsidiary rea-

soning, that irresistible conviction which demonstra-

tion necessarily commands ?

It furnishes no valid reply to this objection, to al-

lege, that mathematicians often employ themselves

in inventing different demonstrations of the same

theorem j for, in such instances, their attempts do

not proceed from any anxiety to swell the mass of

evidence, by finding (as in some other sciences) a va-

riety of collateral arguments, all bearing, with their

combined force, on the same truth ;—their only

wish is, to discover the easiest and shortest road by

which the truth may be reached. In point of sim-

plicity, and of what geometers call elegance^ these

various demonstrations may differ widely from each

other ; but, in point of sound logic, they are all pre-

cisely on the same footing. Each of them shines

with its own intrinsic light alone ; and the first

which occurs (provided they be all equally under-

stood) commands the assent not less irresistibly than

the last.

The idea, however, on which Aristotle proceeded,

in attempting to fortify one demonstration by ano-

ther, bears no analogy whatever to the practice of

expedient for exposing, to the incaucst understanding, the futi-

lity of the syllogistic theory.

262 ELEMENTS OF TtTE PHILOSOPHY Chap. Hi,

mathematicians in multiplying proofs of the same

theorem ; nor can it derive the slightest countenance

from their example. His object was not to teach us

how to demonstrate the same thing in a variety of dif-

ferent ways ; but to demonstrate, by abstract reason-

ing, the conclusiveness of demonstration. By what

means he set about the accomplishment of his pur-

pose, will afterwards appear. At present, I speak

only of his design ; which, if the foregoing remarks

be just, it will not be easy to reconcile with correct

views, either concerning the nature of evidence, or

the theory of the human understanding.

For the sake of those who have not previously

turned their attention to Aristotle's Logic, it is ne-

cessary, before proceeding farther, to take notice of

a peculiarity (and, as appears to me, an impropriety)

in the use which he makes of the epithets demon-

strative and dialectical^ to mark the distinction be-

tween the two great classes into which he divides

syllogisms ; a mode of speaking which, according to

the common use of language, would seem to imply,

that one species of syllogisms may be more conclu-

sive and cogent than another. That this is not the

case, is almost self-evident \ for, if a syllogism be

perfect inform^ it must, of necessity, be not only

conclusive, but demonstrati , ely conclusive. Nor is

this, in fact, the idea which Aristotle himself an-

nexed to the distinction ; for he tells us, that it

does not refer to \X\QJorm of syllogisms, but to their

matter ;—or, in plainer language, to the degree of

evidence accompanying the premises on which they

10


proceed. * In the two books of his last Analytics,

accordingly, he treats of syllogisms which are said

to be demonstrative, because their premises are cer-

tain ; and in his Topics, of what he calls dialectical

syllogisms, because their premises are only probable.

Would it not have been a clearer and juster mode of

stating this distinction, to have applied the epithets

demonstrative and dialectical to the truth of the

conclusions resulting from these two classes of syl-

logisms, instead of applying them to the syllogisms

themselves ? The phrase demonstrative syllogism

certainly seems, at first sight, to express rather the

complete and necessary connection between the con-

clusion and the premises, than the certainty or the

necessity of the truths which the premises assume.

To this observation it may be added (in order to

prevent any misapprehensions from the ambiguity of

language), that Aristotle's idea of the nature of de-

monstration is essentially different from that which

I have already endeavoured to explain. *' In all

" demonstration," says Dr Gillies, who, in this in-

stance, has very accurately and clearly stated his

* To the same purpose also Dr Wallis :" Syllogismus Topicus

" (qui et Dialectkus dici solet) talis haberi solet syllogismus (seu

" syllogismorum series) qui firmam potius praisumptionem, seu

" opinionem valde probabilem creat, quam absolutam certitudi-

" nem. Non quidem ratione Formce (nam syllogismi omnes,

" si in justa forma, sunt demonstrativa ; hoc est, si praemissas

" verae sint, vera erit et conclusio), sed ratione Materice, seu

" Prcemissarum ; quae ipsae, utplurimum, non sunt absolute cer-

" tse, et universaliter verae ; sed saltern probabiles, atque utplu-

" riraum verae."

—

JVallisy Loîca, Lib. iii. cap. 23.


author*s doctrine, " the first principles must be ne-

" cessary, immutable, and therefore eternal truths,

** because those qualities could not belong to the

" conclusion, unless they belonged to the premises,

" which are its causes." * According to the ac-

count of demonstrative or mathematical evidence

formerly given, the first principles on which it rests

are not eternal and immutable truths, but definitions

or hypotheses j and, therefore, if the epithet de-

* AiistotJe's Ethics and Politics, &c. By Dr Gillies. Vol. I.

p. 96.

I am much at a loss how to reconcile this account of demon-

strative evidence with the view which is given by Dr Gillies of

the nature of syllogism, and of the principles on which the syllo-

gistic theory is founded. In one passage (p. 81.), he tells us, that

" Aristotle invented the syllogism, to prevent imposition arising

" from the abuse of words:" in a second (p, 83.) that " the sim-

" pic truth on which Aristotle has reared a lofty and various

" structure of abstract science, clearly expressed, and Jullj/ de-

" monstrated—is itself founded in the natural and universal tex-

" ture of language :'' in a third (p. S().)> that " the doctrines of

" Aristotle's Organon have been strangely perplexed by confound-

'' ing the gramtnatical principles on xckich that work is built with

" mathematical axioms." Is it possible to suppose, that Aristo-

tle could have ever thought of applying to mere grammatical

principles,— to truthsfounded in the natural and nniversal texture

of language—the epithets of necessary, immutable, and eternal?

I am unwilling to lengthen this note, otherwise it might be

easily shewn, how utterly irreconcilable, in the present instance,

are the glosses of this ingenious commentator with the text of his

author. Into some of these glosses it is probable that he has

been unconsciously betrayed, by his anxiety to establish the claim

of his favourite pliilosopher to tlie important speculations of

Locke on the abuse of words, and to those of some later writers on

language considered as an instrument of thought.


iiionstrative be understood, in our present argument,

as descriptive of that peculiar kind of evidence

which belongs to mathematics, the distinction be-

tween demonstrative and dialectical syllogisms is re-

duced to this ; that in the former, where all that is

asserted is the necessary connection between tlie

conclusion and the premises, neither the one nor the

other of these can with propriety be said to be either

true Qvjalse, because both of them are entirely hy-

pothetical ; in the latter, where the premises are

meant to express truths or facts (supported on the

most favourable supposition, by a very high degree

of probability), the conclusion must necessarily par-

take of that uncertainty in which the premises are

involved.

But what I am chiefly anxious at present to im-

press on the minds of my readers, is the substance

of the two following propositions : Fir'st, That dia-

lectical syllogisms (provided they be not sophistical)

are not less demonstratively conclusive, soJar as tlie

process of reasoning is concerned, than those to

which this latter epithet is restricted by Aristotle;

and, secondly. That it is to the process ofreasoning

alone, and not to the premises on which it proceeds,

that Aristotle's demonstrations exclusively refer.

The sole object, therefore, of these demonstrations

is (as I already remarked), not to strengthen, by new

proofs, principles which were doubtful, or to supply

new links to a chain of reasoning which was imper-

fect, but to confirm one set of demonstrations by

means of another. The mistakes into which some

of my readers might have been led by the contrast

Q66 elements of the philosophy Chap. HI,

which Aristotle's language implies between dialecti-

cal syllogisms, and those which he honours with the

title of demonstrative, will, I trust, furnish a suffi-

cient apology for the length of this explanation.

Having enlarged so fully on the professed aim of

Aristotle's demonstrations, I shall dispatch, in a very

few pages, what I have to oflPer on the manner in

which he has carried his design into effect. If the

design be as unphilosophical as I have endeavoured

to shew that it is, the apparatus contrived for its

execution can be considered in no other light than

as an object of literary curiosity. A process of rea-

soning which pretends to demonstrate the legitima-

cy of a conclusion which, of itself, by its own in-

trinsic evidence, irresistibly commands the assent,

must, we may be perfectly assured, be at bottom un-

substantial and illusory, how specious soever it may

at first sight appear. Supposing all its inferences to

be strictly just, it can only bring us round again to

the point from whence tve set out.

The very acute strictures of Dr Reid, in his Ana-

lysis of Aristotle's Logic, on this part of the Syllo-

gistic Theory, render it superfluous for me, on the

present occasion, to enter into any details upon the

subject. To this small, but valuable tract, there-

fore, I beg leave to refer my readers ; contenting

myself with a short extract, which contains a general

and compendious view of the conclusion drawn, and

of the argument used to prove it, in each of the three

figures of syllogisms.

" In the first figure, the conclusion affirais orde-

** nies something of a certain species or individual

;


** and the argument to prove this conchision is, That

" the same thing may be affirmed or denied of the

" whole genus to which that species or individual

" belongs.

" In the second figure, the conclusion is, That

" some species or individual does not belong to such

" a genus ; and the argument is, That some attri-

" bute connnon to the whole genus does not belong

*' to that species or individual.

" In the third figure, the conclusion is, That such

" an attribute belongs to part of a genus ; and the

" argument is, That the attribute in question belongs

** to a species or individual which is part of that

" genus.

" I apprehend that, in this short view, every com" elusion that falls within the compass of the three

" figures, as well as the mean of proof, is compre-

" hended. The rules of all the figures might be

" easily deduced from it ; and it appears that there

" is only one principle of reasoning in ail the three5

" so that it is not strange, that a syllogism of one

" figure should be reduced to one of another figure.

*' The general principle in which the whole ter-r

" minates, and of which every categorical syllogism

*' is only a particular application, is this. That what*' is affirmed or denied of the whole genus may be

" affirmed or denied of every species and individual

" belonging to it. This is a principle of undoubted

" certainty indeed, but of no great depth. Aristor

" tie and all the logicians assume it as an axiom, or

" first principle, from which the syllogistic system,

" as it were, takes its departure , and after a tedious

Q6S elements of the philosophy Chap. III.

" voyage, and great expence of demonstration, it

" lands at last in this principle, as its ultimate

" conclusion. extras hominumf O quantum est

*' in rebus inane /" *

When we compare this mockery of science with

the unrivalled powers of the inventor, it is scarcely

possible to avoid suspecting, that he was anxious to

conceal its real poverty and nakedness, under the

veil of the abstract language in which it was exhibit-

ed. It is observed by the author last quoted, that

Aristotle hardly ever gives examples of real syllo-

gisms to illustrate his rules ; and that his commen-

tators, by endeavouring to supply this defect, have

only brought into contempt the theoiy of their mas-

ter. " We acknowledge," says he, " that this was

" charitably done, in order to assist the conception

" in matters so very abstract ; but whether it was

" prudently done for the honour of the art, may be

" doubted." One thing is certain, than when we

translate any of Aristotle's demonstrations from the

general and enigmatical language in which he states

it, into more familiar and intelligible terms, by ap-

plying it to a particular example, the mystery at

once disappears, and resolves into some self-evident

or identical puerility. It is surely a strange mode

of proof, which would establish the truth of what is

obvious, and what was never doubted of, by means

of an argument which appears quite unintelligible,

till explained and illustrated by an instance perfect-

ly similar to the very thing to be proved.

* This axiom is calledj in scholastic language, the dictum (!•

omni ct dc nnllo.

Sect, 1. ^^ THE HUMAN MIND. 269

" If A," says Aristotle, " is attributed to every B,

** and B to every C, it follows necessarily, that A" may be attributed to every C." * Such is the de-

monstration given of the first mode of the first figure

;

and it is obviously nothing more than the axiom,

called the dictum de omniy concealed under the dis-

guise of an uncouth and cabalistical phraseology.

The demonstrations given of the other legitimate

modes are all of the same description.

In disproving the illegitimate modes, he proceeds

after a similar manner ; condescending, however, in

general, to supply us, by way of example, with three

terms, such as boiiunif habitus^ prudentia ; album,

equus, cygnus ;—^which three terms, we are left, for

our own satisfaction, to form into illegitimate syllo-

gisms of the particular figure and mode which may be

under consideration. The manifest inconclusiveness

of eveiy such syllogism, he seems to have thought,

might assist readers of slower apprehension in per-

ceiving more easily the import of the general propo-

sition. The inconclusiveness, for instance, of those

* Analyt. Prior, cap. iv.

It is obvious, that Aristotle's symbolical demonstrations might

be easily thrown into the form of symbolical syllogisms. The

circumstance which induced him to prefer the former mode of

statement, was. probably that he might avoid the appearance of

reasoning in a circle, by employing the syllogistic theory to de-

monstrate itself. It is curious how it should have escaped him,

that, in attempting to shun this fallacy, he had fallen into another

exactly of the same description ;—that of employing an argu-

ment in the common form to demonstrate the legitimacy of syllo-

gisms, after having represented a syllogistic analysis as the onJj

infallible test of the legitimacy of a demonstration.


modes of the first figure, in which the major is par-

ticular, is thus stated and explained : " If A is or

" is not in some B, and B in every C, no conclusion

*' follows. Take for the terms in the affirmative

" case, goody habit, prudence ; in the negative,

" good, habit, ignorance.''^ * With respect to such

passages as this, Dr Reid has perfectly expressed

my feeling, when he says, ** That the laconic style

" of the author, the use of symbols not familiar, and,

" in place of giving an example, his leaving us to

*' form one from three assigned terms, give such

" embarrassment to a reader, that he is like one

" reading a book of riddles." t Can it be reason-

ably supposed, that so great an obscurity in such a

writer was not the effect of some systematical design ?

From the various considerations already stated, I

might perhaps, without proceeding farther, be en-

titled to conclude, that Aristotle's demonstrations

amount to nothing more than to a specious and im-

posing parade of words ; but the innumerable testi-

monies to their validity, from the highest names,

and the admiration in which they continue to be

held by men of distinguished learning, render it ne-

cessary for me, before dismissing the subject, to un-

fold a little more completely some parts of the fore-

going argument.

It may probably appear to some of my readers su-

perfluous to remark, after the above-cited specimens

* Analyt. Prior, cap. iv.

+ Dr Gillies has attempted a \ indication of the use which

Aristotle, in his demonstrations, has made of the letters of the al-

phabet. For some remarks on this attempt, see Note (L.)

Sect. 1. OV THE HUMAN MiND. 271

of tlie reasonings in question, that not one of these

demonstrations ever carry the mind forward, a single

step, from one truth to another ; but merely from a

general aaiom to some of its particular exemplifica-

tions. Nor is this all ; they carry the mind in a"

direction opposite to that in which its judgments are

necessarily formed. The meaning of a general

axiom, it is well known, is seldom, if ever intelli-

gible, till it has been illustrated by some example ;

whereas Aristotle, in all his demonstrations, pro-

ceeds on the idea, that the truth of an axiom, in

particular instances, is a logical consequence of its

truth, as enunciated in general terms. Into this

mistake, it must be owned, he was not unnaturally

led by the place which is assigned to axioms at the

beginning of the elements of geometry, and by the

manner in which they are afterwards referred to in

demonstrating the propositions. *' Since A," it is

said, " is equal to B, and B to C, A is equal to C ;

'^Jbr^ things which are equal to one and the same

" things are equal to one another.^* This place, I

have little doubt, has been occupied by mathematical

axioms, as far back, at least, as the foundation of the

Pythagorean school ; and Aristotle*s fundamental

axiom will be found to be precisely of the same de-

scription. Instead, therefore, of saying, with DrGillies, that " on the basis of one single truth Aris-

" totle has reared a lofty and various structure of

*' abstract science,"—it would be more correct to

say, that the whole of this science is comprised or

implied in the terms of one single axiom. Nor must

it be forgotten (if we are to retain Dr Gillies's me-


taphor), that the structure may, with much morepropriety, be considered as the basis of the axiom,

than the axiom of the structure.

When it is recollected, that the greater part of

our best philosophers (and among the rest Dr Reid)

still persevere, after all that Locke has urged on

the opposite side of the question, in considering

axioms as the ground-work of mathematical science,

it will not appear surprising, that Aristotle's de-

monstrations should have so long continued to main-

tain their ground in books of logic. That this idea

is altogether erroneous, in so far as mathematics is

concerned, has been already sufficiently shewn ; the

whole of that science resting ultimately, not on

axioms, but on definitions or hypotheses. By those

who have examined my reasonings on this last point,

and who take the pains to combine them with the

foregoing remarks, I trust it will be readily allow-

ed, that the syllogistic theory furnishes no excep-

tion to the general doctrine concerning demonstra-

tive evidence, which I formerly endeavoured to

establish ; its pretended demonstrations being al-

together nugatory, and terminating at last (as must

be the case with eveiy process of thought involving

no data but what are purely axiomatical) in the very

proposition from which they originally set out.

The idea that all demonstrative science must rest

ultimately on axioms, has been borrowed, with many

other erroneous maxim^, from the logic of Aristotle

;

but is now, in general, stated in a manner much

more consistent (although, perhaps, not nearer to

the truth) than in the works of that philosopher.


According to Dr Reid, the degree of evidence

which accompanies our conclusions, is necessarily

determined by the degree of evidence which accom-

panies our first principles ; so that, if the latter be

only probable, it is perfectly impossible that the for-

mer should be certain. Agreeing, therefore, with

Aristotle, in considering axioms as the basis of all

demonstrative science, he was led, at the same time,

in conformity with the doctrine just mentioned, to

consider them as eternal and immutable truths,

which are perceived to be such by an intuitive

judgment of the understanding. Tliis, however, is

not the language of Aristotle ; for, while he tells

us, that there is no demonstration but of eternal

truths,* he asserts, that the first principles which

are the foundation of all demonstration, are got by

induction from the informations of sense.t In what

* âvBôv 8i }o, iocv uffiv a/ rrgorasetg y.xSoXis s^ dv 6 S-oXkoyiSfiog,

er/ avayy.1) xj ro CuiJU'TrigaiSiMot. a'/diov uvai rrig roiavrrig arroBsi^sojc, }y

TTiQ [a.'TrXug n'Ziiv) wrodnîug. ax, itsriv ago, arrodiiîg ruv (p&aoroiv, s6'

iTiSTrifiri dffXw;, aXX' irws, bXS'Xig %ara cu/i/SeSjjJcos*

—

Analyt. Post.

Lib. 1. cap. viii.

+ E;£ fiiv ovv aieSr^Ciug yiyarai /xf^j/jf-Jj. sx hi ,av»i,a?j5 rroXkaxig

Tis aura yivofMivrig, s^wrrsigia. ai yag croXXa/ fivTj/xai rw a^/^/xw, s/x-

C2/g/a /x/a ssrir i% o cihiriiotag y\ sk '^ravTog Ti^sfiTidavrog ra xadoXa iv

rr\ -ûyrj, ra hog iraoa to. rroXka, 6 av iv artagiv h ivr\ exuvoig ro avro,

nyjirig as^yji )u iTiffrrj/j^rig, sav fisv Tsg/ ysviSiv, Tzyjrig' sac h m^^t

ro (iv, i'-ridTriiMYig. {Âvalyt. Post. Lib. ii. cap. xix,) The whole

chapter may be read with advantage by those who wish for a

fuller explanation of Aristotle's opinion on this question. Mis

illustration of the intellectual process by which general prin-

ciples are obtained from the perceptions of sense, and from re-

VOL, II. S

^Z^' ELEMENTS OF THE PHILOSOPHY Chap. III.

manner this apparent contradiction is to be recon-

ciled, I leave to the consideration of his future com-

mentators.

For my own part, I cannot help being of opinion

with Lord Monboddo (who certainly was not want-

ing in a due respect for the authority of Aristotle),

that the syllogistic theory would have accorded

much better with the doctrine of Plato concerning

general ideas, than with that held on the same sub-

ject by the founder of the Peripatetic school.* Tomaintain that, in all demonstration, we argue from

generals to particulars, and, at the same time, to as-

sert, that the necessary progress of our knowledge

is from particulars to generals, by a gradual induc-

tion from the informations of sense, do not appear,

to an ordinary understanding, to be very congruous

parts of the same system ; t and yet the last of these

tenets has been eagerly claimed as a discovery of

iterated acts of memory resolving into one experience, is more

particularly deserving of attention.

* Ancient Metaphysics, Vol. V. pp. 184, 185.

t It may perhaps be asked, Is not this the very mode of phi-

losophizing recommended by Bacon, first, to proceed analytically

from particulars to generals, and then to reason synthetically from

generals to particulars? My reply to this (luestion (a question

which will not puzzle any person at all acquainted with the sub*

ject) I must delay, till I shall have an opportunity, in the pro-

gress of my work, of pointing out the essential diflVrence between

the meanings annexed to the v.ord induction, in the Aristotelian,

and in the Baconian logic. Upon the present occasion, it is

sufficient to observe, that Bacon's plan of investigation was never

supposed to be applicable to the discovery of principles which

are necessary and eternal.

5

S,>ct. I. OF THE HUMAN MIND. 9.^5

Aristotle, by some of the most zealous admirers of

his loirical demonstrations.*

* See Dr Gillies's Analysis of Aristotle's works, passim.

In this Icaniecl, and, on the whole, very instructive perform-

ance, I tind several doctrines ascribed to Aristotle, which appear

not a little at variance with each other. The following passages

(which I am led to select from their connection with the present

argument) gtrike me as not only widely difl'erent, but completely

contradictory, in their import.

" According to Aristotle, definitions are the foundations of all

" science ; bui thosefountains are pure only tvhcn they originate in

" an accurate examination, and patient comparison of the percep-

" tible qualities of individual objects." Vol. I. p. 77-

*' Demonstrative truth can apply only to those things which

" necessarily exist after a certain manner, and whose state is un-

" alterable ; and we know those things when we know their

*' causes: Thus we know a mathematical proposition, when we" know the causes that make it true; that is, when we know all

" the intermediate propositions, up to the first principles or

" axioms, on which it is ultimately built,''' Ibid. pp. QS, 96»

It is almost superfluous to observe, that while the former of

these quotations founds all demonstrative evidence on definitions,

the latter founds it upon axioms. Nor is this all. The former

(as is manifest from the second clause of the sentence) can refer

only to co7itingent truths ; inasmuch as the most accurate exa-

mination of the perceptible qualities of individual objects can

never lead to the knowledge of things which necessarily exist a/'..

ter a certain manner. The latter as obviously refers (and exclu-

sively refers) to truths which resemble mathematical theorems.

As to Aristotle's assertion, that definitions are the first prin-

ciples of all demonstrations {a'l a^yai ruv aTodii^suv o) oîsixoi), it

undoubtedly seems, at first view, to coincide exactly with the

doctrine which I was at so much pains to inculcate, in treating

of that peculiar evidence which belongs to mathematics. I hope,

however, 1 shall not, on this account, be accused of plagiarism,

when it is considered, that the commentary upon these words,

quoted above from Dr Gillies, absolutely excludes mathematics

276 ELEMENTS OF THE PHILOSOPHY Chap. IIL

In this point of view, Lord Monboddo has cer-

tainly conducted, with greater skill, his defence of

the syllogistic theory ; inasmuch as he has entirely

abandoned the important conclusions of Aristotle

concerning the natural progress of human know-

ledge ; and has attempted to entrench himself in

(what was long considered as one of the most inac-

cessible fastnesses of the Platonic philosophy) the

very ancient theory, which ascribes to general ideas

an existence necessary and eternal. Had he, upon

this occasion, after the example of Aristotle, con-

lined himself solely to abstract principles, it might

not have been an easy task to refute, to the satisfac-

tion of common readers, his metaphysical arguments.

Fortunately, however, he has favoured us with some

examples and illustrations, which render this under-

taking quite unnecessary ; and which, in my opi-

nion, have given to the cause which he was anxious

to support, one of the most deadly blows which it

has ever received. The following panegyric, in par-

ticular, on the utility of logic, while it serves to shew

that, in admiration of the Aristotelian demonstra-

tions, he did not yield to Dr Gillies, forms precisely

such a comment as I myself could have wished for,

on the leading propositions which I have now been

attempting to establish.

*' In proof of the utility of logic,*' * says Lord

Irom the number of those sciences to which they are to be ap-

plied. On this point, too, Aristotle's own language is decisive.

E^ amy/Mioiv aoa cu'kKoyid/jiog iCriv 57 a'^robn'tî^,—Analyt. Poster,

Lib. i. cap. iv.

* Ancient Metaphysics, Vol. V. p. 152.


Monboddo, " I will give an example of an argu-

" ment to prove that man is a substance *, which

** argmnent, put into the syllogistic form, is this

:

" Every Animal is a Substance ;

*' JEvery Man is an Animal

;

** Therefore every Man is a Substance."

" There is no man, I believe, who is not con*

" vinced of the truth of the conclusion of this syllo-

" gism : But, how he is convinced of this, and for

" what reason he believes it to be true, no man can

*' tell, who has not learned, from the logic of Aris-

" totle, to know what a proposition, and what a syl-

" logism is. There he will learn, that every propo-

*' sition affirms or denies something of some other

" thing. AVliat is affirmed or denied, is called the

*' Predicate ; and that of which it is affirmed or de-

" nied, is called the Subject. The predicate being

" a more general idea than the subject of which it

" is predicated, must contain or include it, if it be

" an affirmative proposition ; or if it be a negative

" proposition, it must exclude it. This is the nature

" of propositions : And as to syllogism, the use of

" it is to prove any proposition that is not self-evi-

" dent. And this is done by finding out what is

" called a middle term ; that is, a tenn connected

" with both the predicate and the subject of the

" proposition to be proved. Now, the proposition

" to be proved here is, that man is a substance ; or,

" in other words, that substance can be predicated

" of man : And the middle term, by which this

" connection is discovered, is animal, of which sub-

27§ ELEiAIENTS OF THE PHILOSOPHY Chap. III.

" stance is predicated ; and this is the major propo-

*' sition of the syllogism, by which the major term

" of the proposition to be proved, is predicated of

" the middle term, llien animal is predicated of

" man ; and tliis is tlie minor proposition of the

*' syllogism, by which the middle tenn is predicated

*' of the lesser term, or subject of the proposition to

" be proved. The conclusion, therefore, is, that as

" substance contains animal, and man is contained in

" animal, or is part of animal, therefore substance

" contains man. And the conclusion is necessarily

" deduced from the axiom I have mentioned, as the

" foundation of the truth of the syllogism, * That** the whole is greater than any of its parts, and con-

" tains them all.' So that the truth of the syllogism

"is as evident as when we say, that if A contain

" B, and B contain C, then A contains C.

" In this manner Aristotle has demonstrated the

" truth of the syllogism. But a man, who has not

" studied his logic, can no more tell why he believes

" the truth of the syllogism above mentioned, con-

" cerning man being a substance^ than ajoiner, or any

" common mechanic, who applies a foot or a yard to

" the length of two bodies, and finds that both agree

*' exactly to that measure, and are neither longer

" nor shorter, can give a reason why he believes

" the bodies to be equal, not knowing the axiom of

" Euclid, * That two things, which are equal to a

" third thing, are equal to one another.'*'

" By this discovery Aristotle has answered the

" question, which Pontius Pilate, the Roman Go-" vernor, asked of our Saviour, JVhat Truth is?

Sect. 1. 03F THE HUMAN MIND. 579

** The answer to which appears now to be so ob-

" vious, that I am persuaded Pihite would not have

*' asked it as a question, which he no doubt thought

" very difficult to be answered, if he had not studied

" the logic of Aristotle." *

After perusing the above exposition of Aristotle's

demonstration, the reader, if the subject be alto-

gether new to him, will be apt to imagine, that the

study of logic is an undertaking of much less diffi-

culty than he had been accustomed formerly to ap-

prehend ; the whole resolving ultimately into this

ftxiom, " That if A contains B, and B contains C,

* Ancient Metaphysics, Vol. V. pp. 152, 153, 154.

1 have quoted this passage at length, because I consider it as

an instructive example of the effects likely to be produced on

the understanding by scholastic studies, where they become a

favourite and habitual object of pursuit. The author (whom I

knew well, and for whose memory I entertain a sincere respect)

was a man of no common mental powers. Besides possessing a

rich fund of what is commonly called learning, he was dis-

tinguished by natural acuteness ; by a more than ordinary share

of wit; and, in the discharge of his judicial functions, by the

singular correctness, gravity, and dignity of his unpremeditated

elocution;—and yet, so completely had his faculties been

subdued by the vain abstractions and verbal distinctions of the

schools, that he had brought himself seriously to regard such

discussions as that which I have here transcribed from his works,

not only as containing much excellent sense, but as the quint-

essence of sound philosophy. As for the mathematical and

physical discoveries of the Newtonians, he held them in com-

parative contempt, and was probably prevented, by this circum-

stance, from ever proceeding farther than the first eletnents of

these sciences. Indeed, his ignorance of both was wonderful,

considering the very liberal education which he had received,

not only in his own country, but at a foreign university.


" then A contains C." In interpreting this axiom,

he will probably figure to himself A, B, and C, as

bearing some resemblance to three boxes, the sizes

of which are so adapted to each other, that B may-

be literally put into the inside of A, and C into the

inside of B. Perhaps it may be reasonably doubted, if

there is one logician in a hundred, who ever dream-

ed of understanding it in any other sense. Whenconsidered in this light, it is not surprising that it

should instantly command the assent of the merest

novice : Nor would he hesitate one moment longer

about its truth, if, instead of being limited (in con-

formity to the three terms of a syllogism) to the

three letters. A, B, C, it were to be extended from

A to Z ; the series of boxes corresponding to the

series of letters, being all conceived to be nestled,

one within another, like those which we sometimes

see exhibited in the hands of a juggler.

If the curiosity of the student, however, should

lead him to inquire a little more accurately into

Aristotle's meaning, he will soon have the mortifica-

tion to learn, that when one thing is said by the lo-

gician to he in another, or to be contained in another,

these words ai'e not to be understood in their ordi-

nary and most obvious sense, but in a particular and

technical sense, known only to adepts ; and about

which (we may remark by the way) adepts are not,

to this day, unanimously agreed. " To those,'* says

Lord Monboddo, " who know no more of logic nor

*' of ancient philosophy than Mr Locke did, it will

*' be necessary to explain in what sense one idea can

" be said to contain another, or the idea less gencr

Sect. 1. OF THE HUMAN MIND. S81

" ral can be said to be a part of the more general.

" And, in the first place, it is not in the sense that

" one body is said to be a part of another, or the

" greater body to contain the lesser ; nor is it as one

" number is said to contain another ; but it is vir-

" tuall^ or potentially that the more general idea

" contains the less general. In this way the genus

" contains the species ; for the genus may be pre-

" dicated of every species under it, whether existing

" or not existing ; so that virtually it contains all

" the specieses under it, which exist or may exist.

" And not only dofes the more general contain the

** less general, but (what at first sight may appear

" surprising) the less general contains the mt)re ge-

" neral, not virtually or 'potentially, but actually.

" Thus, the genus animal contains virtually man,

'* and eveiy other species of animal either existing

" or that may exist : But the genus animal is contain-

*' ed in man, and in other animals actually ; for man*' cannot exist without being in actuality^ and not

*' potentially only an animal.'* *

* Ancient Metaphysics, Vol. IV. p. 73.

For the distinction betwixt containing potentially and actually/.

Lord INIonboddo acknowledges himself indebted to a Greek au-

thor then living, Eugenius Diaconus. {Jnc. Met. Vol. IV. p.

73.) Of this author we are elsewhere told, that he was a Pro-

fessor in the Patriarch's University at Constantinople ; and that

he published, in pure Attic Greek, a system of logic, at Leipsic,

in the year 1766. (Origin and Progress of Language, Vol. I.

p. 45, 2d edit.) It is an extraordinary circumstance, that a dis-

covery, on which, in Lord Monboddo's opinon, the whole truth of

the syllogism depends^ should have been of so very recent a date.


If we have recourse to Dr Gillies lor a little more

light upon this question, we shall meet with a similar

disappointment. According to him, the meaning

of the phrases in question is to be sought for in the

following definition of Aristotle :" To say that one

" thing is contained in anotl.er, is the same as say-

" ing, that the second can be predicated of the first

" in the full extent of its signification ; and one

" term is predicated of another in the full extent of

" its signification, when there is no particular de-

*' noted by the subject, to which the predicate does

" not apply." * In order, therefore, to make sure

of Aristotle's idea, we must substitute the defini-

* Gillies's Aristotle, Vol. I p. 73. " This remark," says Dr

Gillies, ^ which is the foundation of all Aristotle s logic, has been

" sadly ii;istaken by many. Among others, Dr Ileid accuses

" Aristotle of using as synonymous phrases, the being in a sub-

" ject, and the being truly predicated of a subject ; whereas the

" truth is, that, according to Aristotle, the meaning of the one

" phrase is directly the reverse of the meaning of the other."

—

Ibid.

While I readily admit the justness of this criticism on Dr Reid,

I must take the liberty of adding, that I consider Reid's error as

a mere oversight, or slip of the pen. That he might have accus-

ed Aristotle of confounding two things which, although different

in fact, had yet a certain degree of resemblance or affinity, is by

no means impossible : but it is scarcely conceivable, that he

could be so careless as to accuse him of confounding two things

Avhich he invariably states in direct opposition to each other.

J have not a doubt, therefore, that Reid's idea was, that Aristo-

tle used, as synonymous phrases, the being in a thing, and the

being a subject of which that thing can be truly predicated ; more

especially, as either statement would equally well have answered

his purpose.

Sect. 1

.

OF THE HUMAN MIND. ^8?

tion instead of the thing defined ; that is, instead of

saying that one thing is contained in another, we

must say, that " the second can be predicated of the

" first in the full extent of its signification." In

this last clause, I give Aristotle all the advantage of

Dr Gillies's very paraphrastical version ; and yet,

such is the effect of the comment, that it at once

converts our axiom into a riddle, I do not say that,

when thus interpreted, it is altogether unintelligi-

ble ; but only that it no longer possesses the same

sort of evidence which we ascribe to it, while we

supposed that one thing was said by the logician to

be contained in another, in the same sense in which

a smaller box is contained in a greater. *

To both comments the same obsei-vation may be

applied ; that, the moment a person reads them, he

must feel himself disposed to retract his assent to

the axiom which they are brought to elucidate ; in-

asmuch as they must convince him, that what ap-

peared to be, according to the common signification

of words, little better than a truism^ becomes, when

translated into the jargon of the schools, an in-

comprehensible, if not, at bottom, an unmeaning

(enigma.

* It is worthy of observation, that Condillac has availed him-

self of the same metaphorical anil equivocal word, which the

foregoing comments profess to explain, in support of the theory

which represents every process of sound reasoning as a series of

identical propositions. '' L'Analyse est la mcme dans toutes les

" sciences, parce que dans toutes clic conduit du connu a I'in-

" connu par le raisonnemcnt, c'est-a-dire, par une suite de juge-

'' mens qui sont renfermes Ics uns dans les autres." La Logique.

284 ELEMENTS OP THE PHILOSOPHY Chap. IIL

I have been induced to enlarge, with more mi-

nuteness than I could have wished, on this funda-

mental article of logic, that I might not be accused

of repeating those common-place generalities which

have, of late, been so much complained of by Aris-

totle's champions. I must not, however, enter any

farther into the details of the system ; and shall

therefore proceed, in the next section, to offer a few

remarks of a more practical nature, on the object

and on the value of the syllogistic art.

Section II.

General Reflections on the Aim of the Aristotelian

Logicy and on the intellectual Habits xvhich the

study of it has a tendency to form.—That the

improvement of the power of reasoning ought

to be regarded as 07ily a secondary Object in

the cidture of the Understariding.

The remarks which were long ago made by Lord

Bacon on the inutility of the syllogism as an organ

of scientific discovery, together with the acute stric-

tures in Mr Locke's Essay on this form of reason-

ing, are so decisive in point of argument, and, at the

same time, so familiarly known to all who turn their

attention to philosophical inquiries, as to render it

perfectly unnecessary for me, on the present occa-

sion, to add anything in support of them. I shall,

therefore, in the sequel, confine myself to a few very

ireneral and miscellaneous reflections on one or two

points overlooked by these eminent writers ; but to

which it is of essential importance to attend, in or-


der to estimate justly the value of the Aristotelian

logic, considered as a branch of education. *

It is an observation which has been often repeated

since Bacon's time, and which, it is astonishing,, was

so long in forcing itself on the notice of philosophers,

Tliat, in all our reasonings about the established or-

der of the universe, experience is our sole guide, and

knowledge is to be acquired only by ascending from

particulars to generals ; whereas the syllogism leads

us invariably from universals to particulars, the truth

of which, instead of being a consequence of the uni-

versal proposition, is implied and presupposed in the

very terms of its enunciation. The syllogistic art,

therefore, it has been justly concluded, can be of no

use in extending our knowledge of nature, t

* To some of my readers it may not be superfluous to recom-

mend, as a valuable supplement to the discussions of Locke and

Bacon concerning the syllogistic art, what has been since written

on the same subject, in farther prosecution of their views, by Dr

Held in his Analysis of Aristotle's Logic, and by Dr Campbell in

his Philosophy t)f Rhetoric.

\ On this point it would be a mere waste of time to enlarge,

as it has been of late explicitly admitted by some of the ablest

advocates for the Organon of Aristotle. " When Mr Locke," I

quote the words of a very judicious and acute logician, " v/hen Mr" Locke says—' I am apt to think, that he who should employ all

" the force of his reason only in brandishing of syllogisms, will

*' discover very little of that mass of knowledge, which lies y€t

" concealed in the secret recesses of nature ;'—he expresses him-

" self with needless caution. Such a man will certainly not dis-

" cover any of it. And if any imagined, that the mere brcmdish-

'* ing of syllogisms could increase their knowledge (as some of

*' the schoolmen seemed to think), they were indeed very absurd."

^86 ELEMENTS OF THE PHILOSOPHY Chap. IIL

To this observation it may be added, That, if

there are any parts of science in whicli the syllogism

can be advantageously applied, it must be those where

our judgments are formed, in consequence of an ap-

plication to particular cases of certain maxims which

we are not at liberty to dispute. An example of this

occurs in the practice of Law. Here, the particular

conclusion must be regulated by the general prin-

ciple, whether right or wrong. The case was simi-

lar in every branch of philosophy, as long as the au-

thority of great names prevailed, and the old scho-

lastic maxims were allowed, without examination, to

pass as incontrovertible truths. * Since the import-

(^Commejitaiy on the Compendium of Logic used in the University

of Dublin. By the Rev. John Walker. Dublin, 1805.

To the same effect, it is remarked, by a later writer, with re-

spect to Lord Bacon's assertion, " that discoveries in Natural Phi-

" losophy are not likely to be promoted by the engine of syllo-

" gism ;".—" that this is a proposition which no one of the pre-

" sent day disputes ; and which, when alleged by our adversa-

" ries as their chief objection to the study of logic, only proves

*' that they are ignorant of the subject about which they are

" speaking, and of the manner in which it is 7tow taught." (See

an Anonymous Pamphlet printed at Oxford in 1810, p. SO.) Dr

Gillies has expressed himself in terms extremely similar upon va-

rious occasions, (See, in particular, Vol. I. pp. 63, 64, 2d edit.)

This very important concession reduces the question about the

utility of the Aristotelian logic within a very narrow compass.

* " Ce sera un sujet tternel d'etonnement pour Ics personnes

" qui savent bien ce que c'est que philosophic, que de voir que" I'autorite d'Aristote a ele tellement respeclee dans les ecoles

" pendant quelques siecles, que lors qu'un disputant citoit un

" passage de ce philosophe, celui qui soutenoit la these n'osoit


ance of experiment and observation was fully under-

stood, the syllogistic art has gradually fiiUen into

contempt.

A remark somewhat similar occurs in the preface

to the Novum Organoii. " They who attributed so

" much to logic," says Lord Bacon, *' perceived

" very well and truly, that it was not safe to trust the

" understanding to itself, without the guard of any

" rules. But the remedy reached not the evil, but

" became a part of it : jPor the logic which look

" placcy though it might do well enough in civil of-

**Jhirs, and the arts which consisted in talk and opi-

" nio7i, yet comes very far short of subtilty, in the

" real performances of nature ; and, catching at

" what it cannot reach, has served to confirm and es-

** tablish errors, rather than open a way to truth." *

" point dire transeat ; il falloit qu'il niat le passage, ou qu'il

' rexpliquidt a sa manifere." Diet, de Bayle. Art. Aristote.

* As the above translation is by Mr Locke, who has introdu-

ced it in the way of apology for the freedom of his own strictures

on the school logic, the opinion which it expresses may be con-

sidered as also sanctioned by the authority of his name, {See the

Introduction to his Treatise on the Conduct of the Understanding.)

I cannot forbear remarking, on this occasion, that when Lord

Bacon speaks of the school logic as " answering well enough in

" civil affairs, and the arts which consist in talk and opinion,'*

his words can only apply to dialectical syllogisms, and cannot

possibly be extended to those which Aristotle calls demonstrative.

Whatever praise, therefore, it may be supposed to imply, must be

confined to the Books of Topics. The same observation will be

found to hold with respect to the greater part of what has beeii

alleged in defence of the syllogistic art, by Dr Gillies, and by the

other authors referred to in the beginning of this section. One of

the ablest of these seems to assent to an assertion of Bacon, *' Thaf


It is not, however, merely as a useless or ineffi-

cient organ for the discovery of truth, that this art

is exceptionable. The importance of the very ob-

ject at which it professedly aims is not a little doubt-

ful. To exercise with correctness the powers of de-

duction and of argumentation ; or, in other words,

to make a legitimate inference from the premises be-

fore us, would seem to be an intellectual process

which requires but little assistance from rule. Thestrongest evidence of this is the facility with which

men of the most moderate capacity learn, in the

course of a few months, to comprehend the longest

mathematical demonstrations ; a facility which, when

contrasted with the difficulty of enlightening their

minds on questions of morals or of politics, affijrds a

sufficient proof, that it is not from any inability to

conduct a mere logical process, that our speculative

errors arise. The fact is, that, in most of the

sciences, our reasonings consist of a very few steps

;

and yet how liable are the most cautious, and the

most sagacious, to form erroneous conclusions

!

To enumerate and examine the causes of these

false judgments is foreign to my purpose in this sec-

tion. The following (which I mention only by way

of specimen) seem to be among the most powerful.

1. The imperfections of language, both as an instru-

ment of thought, and as a medium of philosophical

" logic does not help towards the invention of arts and sciences,

" but only of arguments." If it only hcljjs towards the invention

of arguments, for what purpose has Aristotle treated so fully of

demonstration and of science in the two books of the Last Ana-

lytics ?

12

Sect. 2. OF THE HUMAN MIND. 28D

communication. 2. The difficulty, in many of our

most important inquiries, of ascertaining they^'c^^ on

which our reasonings are to proceed. 8. The par-

tial and narrow views, which, from want of infoniia-

tion, or from some defect in our intellectual compre-

hension, we are apt to take of subjects, which are

peculiarly complicated in their details, or which are

connected, by numerous relations, with other ques-

tions equally problematical. And lastly (what is

of all, perhaps, the most copious source of specula-

tive error), the prejudices which authority and

fashion, fortified by early impressions and associa-

tions, create to warp our opinions. To illustrate

these and other circumstances by which the judg-

ment is apt to be misled in the search of truth, and

to point out the most effectual means of guarding

against them, would form a very important article

in a philosophical system of logic ; but it is not on

such subjects that we are to expect information from

the logic of Aristotle. *

The fundamental idea on which this philosopher

evidently proceeded, and in which he has been too

implicitly followed by many even of those who have

rejected his syllogistic theory, takes for granted, that

the discovery of truth chiefly depends on the reason-

ing faculty, and that it is the comparative strength

* In the Logic oi Port-Royal, there is a chapter, entitled, Des

sophismcs d'amuitr propre, d'intertf, et de passion, which is well

worthy of a careful perusal. Some useful hints may be also col-

lected from Gravesande's Introdiictio ad PJdlosophiam. Soe Bonk

ii. Part ii. {De Causis Errorum )

VOL. II. T


of this faculty which constitutes the intellectual su-

periority of one man above another. The similarity

between the words reason and reasonings of which

I formerly took notice, and the confusion which ifc

has occasioned in their appropriate meanings, has

contributed powerfully to encourage and to perpe-

tuate this unfortunate mistake. If I do not great-

ly deceive myself, it will be found, on an accurate

examination of the subject, that, of the different ele-

ments which enter into the composition of reason,

in the most enlarged acceptation of that word, the

power of carrying on long '^voce^ê%oi reasoning or

deduction is, in point of importance, one of the

least.*

* It was before observed (pp. 147, 148.), " Thattlie whole theory-

" of syHogisin proceeds on the supposition, that the same word is

" always to be employed in the same sense ; and that, conse-

" cjuently, it takes for granted, in every rule which it furnishes

" for the guidance of our reasoning powers, that the nicest, and

" by far the most difficult part of the logical process, has been

" previously brought to a successful termination."

In this remark (which, obvious as it may seem, has been very

generally overlooked), I have found, since the [foregoing sheets

were printed, that I have been anticipated by M. Turgot. "Tout" I'artifice dh Ce (?alcul ingenieux, dont Aristote nous a donne

" Ics regies, tout I'art du s^llogismo est fond6 sur'"l'usage des

" mots dans ic meme sens ; I'emploi d'un memo mot dans de'ix

" sens difi'erens faitde toutraisoniiement uu sophisme; et ce genre

" de sophisme, peut-etre le plus commun de tous, est une de's

" sources les plus ordinaircs de nos errcurs." Oeuvres de M.

Tvrgot, Tom. III. p. 66.

Lord Bacon had manifestly the same conclusion in view, in the

following aphorism :" Syllogism consists of propositions, propo-

^' sitions of words, and words arc the signs of notions ; therefore,

Sect. Q. OF THE HUMAN MIND. ^1The slightest reflection, indeed, may convince us

how very little connection the mere reasoning faculty

has with the general improvement of mankind. The

wonders which it has achieved have been confined,

in a great measure, to the mathematical sciences,

—

the only branches of human knowledge which fur-

nish occasion for long concatenated processes of

thought ; and even there, 7nethody together with a

dexterous use of the helps to our intellectual facul-

ties which art has discovered, will avail more than

the strongest conceivable capacity, exercised solely

and exclusively in habits of synthetic deduction.

The tendency of these helps, it may be worth while

to add, is so far from being always favourable to the

power of reasoning, strictly so called, that it may be

questioned, whether, among the ancient Greek geo-

meters, this power was not in a higher state of cul-

tivation, in consequence of their ignorance of the

algebraical symbols, than it exists in at this day

among tlie profoundest mathematicians of Europe.

In the other sciences, however, the truth of the

femark" is far more striking. By whom was ever the

art of reasoning so sedulously cultivated as by the

schoolmen, and where shall we find such monuments

" if our notions, the basis of all, are confined, and over hastily

" taken from things, nothing that is built on them can be firm;

" whence our only hope rests uôn geiiuine induction." Nov. Org.

fcvrtl. Sect. 1. Aph. 14. (Shaw's Translation.)

On what erounrls Dr Gillies was led to hazard the assertion

formerly quoted (p 264.), that " Aristotle invented the syllogism,

" to prevent imposition arising from the abuse of words," I am«uite unable to form a conjecture. -

ELEMENTS OF THE PHILOSOPHY Cliap. III.

of what 7nere reaso7iing can accomplish, as in their

writings ? Whether the same end might not have

been attained without the use of their technical rules,

is a different question ; but that they did succeed, to

a great degree, in the acquisition of the accomplish-

ments at which they aimed, cannot be disputed.

And yet, I believe, it will be now very generally ad-

mitted, that never were labour and ingenuity em-

ployed, for so many ages, to so little purpose of real

utility. The absurdity of expecting to rear a fabric

of science by the art of reasoning alone, was remark-

ed, with singular sagacity, even amidst the darknessf

of the twelfth century, by Jolin ofSalisbury ^ himself

a distinguished proficient in scholastic learning,

which he had studied under the celebrated Abelard.

*' After a long absence from Paris," he tells us in

one passage, " I went to visit the companions of my" early studies. I found them, in every respect,

*' precisely as I had left them ; not a single step ad-

" vanced towards a solution of their old difficulties,

" nor enriched by the accession of one new idea :•

—

" a strong experimental proof, that, how much so-

" ever logic may contribute to the progress of other

" sciences, it must for ever remain barren and life-

" less, while abandoned to itself." *

Among the various piu'suits now followed by men

liberally educated, there is none, certainly, which

•affords such scope to the reasoning faculty, as the

science and profession of law ; and, accordingly, it

has been observed by Mr Burke, *' That they do

* Metalog. Lib. ii. cap. 10.


" more to quicken and invigorale the understand-

**iiigi than all the other kinds of learning put to-

** gether." The same author, however, adds, that

" they are not apt, except in persons very happily

" born, to open and to liberalize the mind, exactly

" in the same proportion." Nor is this suqirising ;

for the ultimate standards of right and wrong, to

which they recognise the competency of an appeal,

being conventional rules and human authorities, no

jfield is opened to that spirit of free inquiry which it

is the boast of philosophy to cultivate. The habits

of thought, besides, which the long exercise of the

profession has a tendency to form, on its appropri-

ate topics, seem unfavourable to the qualities con-

nected with what is properly called judgment

;

or, in other words, to the qualities on which the

justness or correctness of our opinions depends

:

they accustom the mind to those partial views of

things which are suggested by the separate interests

of litigants ; 7iot to a calm, comprehensive, and dis-

criminating survey of details, in all their bearings

and relations. Hence the apparent inconsistencies

which sometimes astonish us in the intellectual cha-

racter of the most distinguished practitioners,—

a

talent for acute and refined distinctions;powers of

subtle, ingenious, and close argumentation ; inex-

haustible resources of invention, of wit, and of elo-

quence ;—combined, not only with an infantine im-

becility in the affairs of life, but with an incapacity

of forming a sound decision, even on those proble-

matical questions which are the subjects of their daily

discussion. The great and enlightened minds.


whose judgments liave been transmitted to posterity,

as oracles of legal wisdom, were formed (it may be

safely presumed), not by the habits of their profes-

sional warfare, but by contending with these habits,

and shaking off their dominion.

The habits of a controversial writer are, in some

respects, analogous to those of a lawyer ; and their

effects on the intellectual powers, when engaged in

the investigation of truth, are extremely similar.

They confine the attention to one particular view of

the question, and, instead of training the under-

standing to combine together the various circum-

stances which seem to favour opposite conclusions,

so as to limit each other, and to guard the judgment

against either extreme,—they are apt, ])y presenting

the subject sometimes wholly on the one side, and

sometimes wholly on the other, to render the dispu-

tant the sceptical dupe of his own ingenuity. Such

seems to have been nearly the case with the redoubt-

able Chillingworth ; a person to whose native can-

dour the most honourable testimony has been born

by the most eminent of his contemporaries, and

whose argumentative powers have almost become

matter of proverbial remark. Dr Reid has pro-

nounced him the " best reasoner, as well as the

" acutest logician of his age ;" and Locke himself

has said, " If you would have your son to reason

" well, let him read Chillingworth." To what con-

sequences these rare endowments and attainments

led, we may learn from Lord Clarendon.

*' Mr Chillingworth had spent all his younger

?" time in disputations, and had arrived at so great a

beet. Vl. OF THE HUMAN MIND. 295

" mastery, that he was inferior to no man in those

" skirmishes : but he had, with his notable perfec-

" tion in this exercise, contracted such an irresolu-

" tion and habit of doubting, that by degrees he

*' grew confident of nothing." ** Neither the

*' books of his adversaries, nor any of their persons,

" though he was acquainted with the best of both,

*' had ever made great impression on him ; all his

*' doubts grew out of himself, when he assisted his

^* scruples with all the strength of his own reason,

^* and was then too hard for himself: but finding as

*' little quiet and repose in those victories, he quick-

" ly recovered, by a new appeal to his own judg-

" ment ; so that, in truth, he was, in all his sallies

*' and retreats, his owti convert."

The foregoing observations, if well founded, con-

clude strongly, not merely against the form of the

school logic, but against the importance of the end

to which it is directed. Locke and many others

have already sufficiently shewn, how inadequate the

syllogistic theory is to its avowed purpose ; but few

seem to be sufficiently aware, how very little this

purpose, if it were attained, would advance us in tlie

knowledge of those truths which are the most inte-

resting to human happiness.

" There is one species of madman," says Father

Buffier, '* that makes an excellent logician." *

—

The remark has the appearance of being somev/hat

paradoxical ; but it is not without a solid foundation,

both in fact, and in the theoiy of the human under-

* Tniile t!os Picm. Veriios. Part I. chap. xi.

^96 ELEMENtS OF THE PHILOSOPHY Chap. III.

Standing. Nor does it apply merely (as Buffier

seems to have meant it) to the scholastic defenders

of metaphysical paradoxes ; it extends to all whose

ruling passion is a display of argumentative dexteri-

ty, without much solicitude about the justness of

their premises, or the truth of their conclusions. It

is observed by Lord Erskine, in one of his admirable

pleadings lately published, that " in all the cases

*' which have filled Westminster-Hall with the most

*' complicated considerations—^the lunatics, and

" other insane persons who have been the subjects

*' of them, have not only had the most perfect know-*' ledge and recollection of all the relations they

*' stood in towards others, and of the acts and cir-

*' cumstances of their lives, but have, in generaly

" been rêmarkable for subtlety and acuteness.^^—" These," he adds, *' are the cases which frequent-

*' ly mock the wisdom of the wisest in judicial trials ;

*' because such persons often reason with a subtlety

" which puts in the shade the ordinary conceptions

*' ofmankind : their conclusions are just, and fre-

*' quently profound j but the premises from which

" they reason, when within the range ofthe malady^

*' are uniformly false :—not false from any defect

" of knowledge or judgment ; but because a delusive

*' image, the inseparable companion of real insanity,

" is thrust upon the subjugated understanding, in-

•' capable of resistance, because unconscious of at-

'* tack.'*

In the instances here alluded to, something, it is

probable, ought to be attributed to the physical in-

fluence of the disorder in occasioning, together with

Sect. 2. 0¥ THE HUMAN MIND, ^97

an increased propensity to controversy, a preterna-

tural and morbid excitation of tlie power of attention,

and of some other intellectual faculties ; but muchmore, in my opinion, to its effects in removing the

check of those collateral circumstances by which, in

more sober understandings, the reasoning powers are

perpetually retarded and controlled in their opera-

tion. Among these circumstances, it is sufficient

to specify, for the sake of illustration, 1. That dis-

trust, which experience gradually teaches, of the ac-

curacy and precision of the phraseology in which

our reasonings are expressed ;—accompanied with

a corresponding apprehension of involuntary mis-

takes from the ambiguity and vagueness of language

;

^, A latent suspicion, that we may not be fully in

possession of all the elements on which the solution

of the problem depends ; and 8. The habitual influ-

ence of those first principles of propriety, of morali-

ty, and of common sense, which, as long as reason

maintains her ascendant, exercise a paramount au-

thority over all those speculative conclusions which

have any connection with the business of life. Ofthese checks or restraints on our reasoning process-

es, none are cultivated and strengtiicned, either by

the rules of the logician, or by the habits of viva voce

disputation. On the contrary, in proportion as their

regulating power is confirmed, that hesitation and

suspense of judgment are encouraged, which are so

congenial to the spirit of true philosophy, but such

fatal encumbrances in contending with an antago-

nist whose object is not truth but victory. In mad-

ness, where their control is entirely thrown off, the

298 ELEMENTS jOF THE PHILOSOPHY Chap. 111.

iBereiy logical process (which never stops to analyse

the meaning of words) is likely to go on more rapid-

ly and fearlessly than before ;—producing a volubi-

lity of speech, and an apparent quickness of concep-

tion, which present to common observers all the

characteristics of intellectual superiority. It is scarce-

ly necessaiy to add, that the same appearances,

which, in this extreme case of mental aberration, are

displayed on so great a scale, may be expected to

shew themselves, more or less, wherever there is any

deficiency in those qualities which constitute depth

and sagacity of judgment.

For my own part, so little value does my indivi-

dual experience lead me to place on argumentative

address, when compared with some other endow-

ments subservient to our intellectual improvement,

that I have long been accustomed to consider that

promptness of reply, and dogmatism of decision,

which mark the eager and practised disputant, as al-

most infallible symptoms of a limited capacity ; a

capacity deficient in what Locke has called (in very

significant, though somewhat homely terms) large,

sound, roundabout sense, * In all the higher en-

dowments of the understanding, this intellectual

quality (to which nature as well as education must

liberally contribute) may be justly regarded as an

essential ingredient. It is this which, when culti-

vated by study, and directed to great objects or pur-

suits, produces an unprejudiced, comprehensive, and

efficient mind ; and, where it is wanting, though

* Conduct of ih'- ri:clcrstnii(fii)". § 3.

S.ecf. 2. OF THE HUMAN MIND. 299

we may occasionally find a more than ordinary share

of quickness and of information ; a plausibility and

brilliancy of discourse ; and that passive susceptibi-

lity of polish from the commerce of the world,

which is so often united with imposing but seconda-

ry talents,—we may rest assured, that there exists a

total incompetency for enlarged views and sagacious

combinations, either in the researches of science, or

in the conduct of affairs.*

* The outlines of an intellectual character, approaching near-

ly to this description, is exhibited by Marmonlel in his hig.'ily

finished (and, I have been assured, very faitht'ul) porlr.iit of I\I.

de Britnne. Among the other defects of that unfortunate states-

man, he mentions particularly m« esprit h Jaceties ; by which

expression he seen;is, from the context, to mean a quality of

mind precisely opposite to that described by Locke in ttie words

(juoted above :

—

'' guelques lumieres, mais eparses ; des appergus

" plutut qzie des vues ; it dans hs grands objets, de lajacilite a

" sahlr lis pietits dttails, nulle capacite jwur embrasser Pensem-*' ble." A consciousness of some similar deficiency has sug-

gested to Gibbon (he following criticism on his own juvenile per-

formance, entitled Essai sur VEtnde. It is executed by an im-

partial and masterly hand ; and may perhaps, without much in-

justice, be extended, not only to his Roman History, but to the

distinguishing features of that peculiar cast of genius, which so

strongly marks all his writings.

" The most serious defect of my Essay is a kind of obscurity

"• and abruptness which always fatigues, and may often elude

"the attention of the reader. The (obscurity of many passages

•' is often aft'ectcd ;proceeding from the desire of expressing per-

•• haps a common idea with sententious bre\ity : brevi esse la-

" boro, obscurusjto. Alas ! how fatal has been the imitation of

'•' Montesquieu 1 But this obscurity SGineiimes proceeds from a

•' mixture of ligJd and darkness in ilie mdhors mind ; from /;

300 ELEMENTS OF THE PHILOSOPHY Chap. Ill,

If these observations hold with respect to the art

of reasoning or argumentation, as it is cultivated by

men undisciplined in the contentions of the schools,

they will be found to apply with infinitely greater

force to those disputants (if any such are still to be

found) who, in the present advanced state of hu-

man knowledge, have been at pains to fortify them-

selves, by a course of persevering study, with the

arms of the Aristotelian logic. Persons of the for-

mer description often reason conscientiously with

warmth, from false premises which they are led by

passion, or by want of information, to mistake for

truth. Those of the latter description proceed sys-

tematically on the radical error of conceiving the

reasoning process to be the most powerful instru-

ment by which truth is to be attained ; combined

with the secondary error of supposing that the power

of reasoning may be strengthened and improved by

the syllogistic art.

In one of Lord Kames's Sketches, there is an

amusing and instructive collection of facts to illus-

trate the jjrogrêss of reason ; a phrase, by which

he seems to mean chiefly the progress of good sense,

or of that quality of the intellect which is very sig-

nificantly expressed by the epithet enlightened. Towhat is this progress (which has been going on with

such unexampled rapidity during the two last cen-

turies) to be ascribed ? Not surely to any improve-

ment in the art of reasoning j for many of the most

" jjnrtial ray tvhich strikes upon an angle, instead of spreading

" itself over the surface ofan ohject.'"


melancholy weaknesses which he has recorded, were

exhibited by men, distinguished by powers of discus-

sion, and a reach of thought, whicli have never been

surpassed ; while, on the other hand, the same

weakness would now be treated with contempt by

the lowest of the vulgar. The principal cause, I

apprehend, has been, the general diffusion of know-

ledge (and more especially of experimental know-

ledge) by the art of printing ; in consequence of

which, those prejudices whicli had so long withstood

the assaults both of argument and of ridicule, have

been gradually destroyed by their mutual collision,

or lost in the infinite multiplicity of elementary

truths which are identified with the operations of the

infant understanding. To examine the process by

which truth has been slowly and insensibly cleared

from that admixture of error with which, during the

long night of Gothic ignorance, it was contaminated

and disfigured, would form a very interesting sub-

ject of philosophical speculation. At present, it is

sufficient to remark, how little we are indebted for

our emancijâtion from this intellectual bondage, to

those qualities which it was the professed object of

the school logic to cultivate ; and that, in the same

proportion in which liberality and light have spread

over Europe, this branch of study has sunk in the

general estimation.

Of the ineflScacy of 7nere reasoning in bringing

men to an agreement on those questions wliich, in

all ages, have furnished to the learned the chief

matter of controversy, a very just idea seems to have

been formed by the ingenious author of the follow-

SOS ELEMENTS OF THE PHILOSOPHY Cluip. IH.

ing lines ; who has, at the same time, hinted at a

i-emedy against a numerous and important class of

speculative errors, more likely to succeed than any

which is to be derived from the most skilful applica-

tion of Aristotle's rules ; or, indeed, from any direct

argumentative refutation, how conclusive and satis-

factory soever it may appear to an unbiassed judg-

ment. It must, at the same time, be owned, that

this remedy is not without danger ; and that the

same habits which are so useful in correcting the pre-

judices of the monastic bigot, and so instructive to

all whose principles are sufficiently fortified by re-

flection, can scarcely fail to produce pernicious ef-

fects, where they operate upon a character not pre-

viously formed and confirmed by a judicious edu-

cation.

En parcouiant au loin la planele ou nous sommes,

Que verrons nous ? les torts et les travers des hommcs '

lei c'est un synode, el la c'cst un divan,

Nous verrons le Mufti, le Derviche, Tlman,

Le Bonze, le Lama, le Talapoin, le Pope,

Les antiques Rabbins et les Abbes d'Europe,

Nos moines, nos prelats, nos docteurs agieges ;

Etes vous disputeurs, mes amis ? voyagez. *

To these verses it may not be altogether useless

to subjoin a short quotation from Mr Locke ; in

whose opinion the aid oi'/otêign travel seems to be

less necessary for enlightening so7?ie of the classes of

controversialists included in the foregoing enumera-

tion, than was suspected by the poet. The moral of

* Discours sur les Disputes, par M. dc Uulhieic.

3

Sect. 2. OF THE HUMAN MIKD. 303

the passage (if due allowances be made for the sati-

rical spirit which it breathes) is pleasing on the

whole, as it suggests the probability, that our com-

mon estimates of the intellectual darkness of our

own times are not a little exaggerated.

" Notwithstanding the great noise that is made

" in the world about errors and opinions, I must do

*' mankind that right as to say, There are not so

'* many men in errors and wrong opinions as is

" commonly supposed. Not that I think they em-

*' brace the truth ; but, indeed, because concerning

*' those doctrines they keep such a stir about, they

" have no thought, no opinion at all. For if any

'* one should a little catechize the greatest part of

" the partizans of most of the sects in the world, he

" would not find, concerning those matters they are

,t' so zealous for, that they have any opinion of their

" own : much less would he have reason to think

" that they took them vipon the examination of ar-

•' guments and appearance of probability. They*' are resolved to stick to a party that education or

" interest has engaged them in ; and there, like the

"' common soldiers of an army, shew their courage

*' and warmth as their leaders direct, without ever

" examining, or so much as knowing, the cause they

" contend for. If a man's life shews that lie has no*' serious regard for religion, for what reason should

*' we think that he beats his head about the opinions

" of his church, and troubles himself to examine the

" grounds of this or that doctrine ? 'Tis enough for

'* him to obey his leaders, to have his hand and his

" tongue ready for the support of the common cause,

304? ELEMENTS OP THE PHILOSOPHY Chap. III.

" and thereby approve himself to those who can

*< give him credit, preferment, and protection in that

" society. Thus men become combatants for those

" opinions they were never convinced of; no, nor

" ever had so much as floating in their heads ; and

" THOUGH ONE CANNOT SAY THERE ARE FEWER IM-

" PROBABLE OR ERRONEOUS OPINIONS IN THE WORLD" THAN THERE ARE, YET THIS IS CERTAIN, THERE" ARE FEWER THAT ACTUALLY ASSENT TO THEM,

" AND MISTAKE THEM FOR TRUTHS, THAN IS IMA-

" GINED." *

If these remarks of Locke were duly weighed,

they would have a tendency to abridge the number

of controversial writers ; and to encourage philoso-

phers to attempt the improvement of mankind, ra-

ther by adding to the stock of useful knowledge,

than by waging a direct war with prejudices, which

have less root in the understandings, than in the in-

terests and passions of their abettors.

Section III.

In xvhat yêspects the study of the Aristotelian Lo-

gic may he useful to Disputants.—A general ac-

quaintance with itjustly regarded as an essential

accomplisiiment to those tcho are liberally edu-

cated.—Doubts suggested by some late Writers^

concerning A7istotle^s claims to the invention of

the Syllogistic Theory.

The general result of the foregoing reflections is,

That neither the means employed by the school lo-

* Essay on Human Understanding. Book iv. c. 20.

12

Sect. 3. OF THE HUMAN MIl^D. 305

gic for the assistance of the discursivefaculty, nor

the accomplishment of that end, were it really at-

tained, are of much consequence in promoting the

enlargement of the mind, or in guarding it against

the influence of erroneous opinions. It is, how-

ever, a veiy different question, how far this art may

be of use to such as are led by profession or inclina-

tion to try their strength in polemical warfare. Myown opinion is, that, in the present age, it would

not give to the disputant, in the judgment of menwhose suffrage is of any value, the slightest advan-

tage over his antagonist. In earlier times, indeed,

the case must have been different. While the scho-

lastic forms continued to be kept up, and w^hile

schoolmen were the sole judges of the contest, an

expert logician could not fail to obtain an easy vic-

tory over an inferior proficient. No*w, however,

when the supreme tribunal to which all parties must

appeal, is to be found, not *withi7i, but without the

walls of universities ; and when the most learned

dialectician must, for his own credit, avoid all allu-

sion to the technical terms and technical fonns of his

art, can it be imagined that the mere possession of

its rules furnishes him with invisible aid for annoy-

ing his adversary, or renders him invulnerable by

some secret spell against the weajôns of his assail-

ant ? * Were this really the case, one might have

* An argument of this sort, in favour of the Aristotelian logic,

has, in fact, been lately alleged, in a treatise to which I have al-

ready had occasion to refer.

VOL, II. U


exiiected that the advocates who have undertaken

its defence (considering how much their pride was

interested in tlie controversy) would have given us

some better specimens of its practical utility, in de-»

fending it against the unscientific attacks of Bacoij

and of Locke. It is, however, not a little remarkable,

that, in every argument which they have attempted

in its favour, they have not only been worsted by

" Îr Locke seems throughout to Imagine that no use can be

" made of the doctrine of syllogisms, unless by men who deliver

** their reasonings in syllogistic form. That would, indeed, justly

'•' expose a man to the imputation of disgusting pedantry and te«

" diousnt hs. But, in fact, he who never uses an expression bor-

" rowed from the Aristotelic logic, may yet, unobserved, be avail-

" ing himself, in the most important manner of its use, by briqg-

" ing defijiitions, divisions, and arguments, to the test of its"

" rules.

" In liu; mere application of it to the examining of an argu-

^' ment which we desire to refute,—the logician will be able to

•• bring the argument in his own mind to syllogistic form.—He" will ihen have before his view every constituent part of the ar-

" gument; some of which may have been wholly suppressed by

" his antagonist, and others disguised by ambiguity and decla-

*' matiun.—He knows every point in which it is subject to exa-

" mination.—He perceives immediately, by the rules of his art,

" whether the premises may be acknowledged, and the conclu-

*' sion denied, for want of a vis consequentia.—If not, he knows

'' wiure to look for a weakness.—He turns to each of the pre-

" mises, and considers whether they are false, dubious, or equi-

" vocal ; and is thus prepared and directed to expose every weak

" point in the argument with clearness, precision,, and method;

*' and this to those who perhaps are wholly ignorant of the aids

" by which the speaker is thus enabled to carry conviction with

" his discourse "

—

Commentanj on the Compendium of Logic, used

in the University of Dublin. Dublin, 1805.

Sect. 3. ^F THE HUMAN MIND. 307

those vei7 antagonists Avhom they accuse of igno-

rance, but iliirly driven from tlie field of battle. *

* In most of the defences of the school logic which I have seen

the chief weapon employed has been that kind of argument

which, in scholasllc phraseology, is called the Argumentum. ad

Uominan ; an argument in the use of which much legard to

consisteixy is seldom to be expected.—In one sentence, accord-

ingly, Baron and Locke arc accused of having never read Aris-

totle ; and, in tlie next, of having borrowed from Aristotle tlie

most valuable part of their writings.

With respect to Locke, it has been triumplumtly observed, that

his acquaintance with Aristotle's logic must have been superfi-

cial, as he has, in one of his objections, manifestly confounded

particular with singular propositions. (Commentary on the Dub-

lin Compendium.) The criticism, I have no doubt, is just; but

docs it, therefore, follow, that a greater familiarity with the tech-

nical niceties of an art which he despised, would have rendered

this profound thinker more capable of forming a just estimate of

its scope and spirit, or of its efficacy in aiding the human under-

standing?—Somewhat of the same description are the attempts

which have been repeatedly made to discredit the strictures of

Dr Reid, by appealing to his own acknowledgment, that there

mio\\t possiblj/ be some parts of the Analytics and Topics which

he had never read. The passage in which this acknowledgment

is made, is so characterislical of the modesty and candour of

the writer, that I am tempted to annex it to this note i—more es-

pecially, as I am persuaded, that, with many readers, it will have

the cflcct of confirming, rather than of shaking, their confidence

in the general correctness and fidelity of his researches.

*' In attemptmg to give some account of the Analytics and of

*' the Topics of Aristotle, ingenuity requires me to confess, iha!;

" though 1 have often purposed to read the whole with care, and

" to understand what is intelligible, yet my courage and patience

" always failed before I had done. Why should I throw away

" so much time and painful attention upon a thing of so little

*' real use ? If I had lived in those ages when the kuojvledge oi


It has, indeed, been asserted by an ingenious and

learned writer, that " he has never met with a per-

" son unacquainted with logic, who could state and

" maintain his argument with facility, clearness, and

" precision ;—that he has seen a man of the acutest

'* mind puzzled by the argument of his antagonist

;

" sensible, perhaps, that it was inconclusive, but

" wholly unable to expose the fallacy which render-

'* ed it so : while a logician, of perhaps very infe-

*' rior talents, would be able at once to discern and*' to mark it.'*

*

I do not deny that there may be some foundation

for this statement. The part of Aristotle's Orga-

non which seems, in the design, to be the most prac-

tically useful (although it is certainly veiy imper-

fect in the execution), is the book of Sophisms j a

*' Aristotle's Organon entitled a man to the highest rank in phi-

" losophy, ambition;might have induced me to employ upon it

*' some years of painful study ; and less, I conceive, would not be

** sufficient. Such reflections as these always got the better of my" resolution, when the first ardour began to cool. All I can say

" is, that I have read some parts of the books with care, some

" slightly, and some perhaps not at all. I have glanced over the

" whole often, and when any thing attracted my attention, have

" dipped into it till my appetite was satisfied. Of all reading,

" it is the most dry and the most painful, employing an infinite

" labour of demonstration, about things of the most abstract na-

" ture, delivered in a laconic style, and often, I think, with af.

" fected obscurity ; and all to prove general propositionsj which,

" when applied to particular instances, appear self-evident.'*

Chap. III. sect. 1.

* Mr Walker, author of the Commentary on the Dublin Com-

pendium of Logic.It


book which still supplies a very convenient phraseo-

logy for marking concisely some of the principal

fallacies which are apt to impose on the understand-

ing in the heat of a titd voce dispute. * Whether it

affords any aid in detecting or discerning these fal-

lacies, may perhaps be doubted. But it is certainly an {

acquisition, and an acquisition ofno contemptible va-

lue, to have always at hand a set of technical terms,

by which we can point out to our hearers, without

circumlocution or discussion, the vulnerable parts of

our antagonist's reasoning. That nothing useful is

to be learned from Aristotle's logic, I am far from

thinking ; but I believe that all which is useful in it

might be reduced into a very narrow compass ; and

I am decidedly of opinion, that wherever it becomes

a serious and favourite object of study, it is infinite-

ly more likely to do harm than good. Indeed, I

cannot help considering it as strongly symptomatic

of some unsoundness in a man's judgment, when I

find him disposed (after all that has been said by

Bacon and Locke)^ to magnify its importance either

* Such phrases, for example, as 1. Fallacia Accidentis. 2. Adicto secundum quid, ad dictum simpliciter. 3. Ab ignorantia Elen-

chi. 4. A non causa pro causa. 5. Fallacia consequentis. 6. Pe~

titio principii. 7- Fallacia pluriurn i/iterrogationum^ SfC.

I have mentioned those fallacies alone which are called by lo-

gicians Fallacies extra Dictioncm ; for as to those which are called

Fallacies in Dictione (such as the Fallacia jEquivocaiionis,

Fallacia Amphibolice, Fallacia Accentus vel Pronunciaiionis,

Fallacia a Figura dictionis, Sfc), they are too contemptible to be

deservino- of any notice.—For some remarks on this last class of

fallacies, See Note (M.)

310 ELEMENTS OF THE PHILOSOPHY Chap. HI.

as an Inventive or as an argumentative Organ. Nordoes this oi)inion rest upon theory alone. It is con-

firmed by all that I have observed (if, after the ex-

ample of the author last quoted, I may presume to

mention the results of my own observations), with

respect to the intellectual characters of the most ex-

pert dialecticians whom I have happened to know.

Among these, I can with great truth say, that al-

though I recollect several possessed of much learn-

ing, subtlety, and ingenuity, I can name none who

have extended by their discoveries the boundaries of

science ; or on whose good sense I should conceive

that much reliance was to be placed in the conduct

of important affairs.

Some very high authorities, I must, at the same

time, confess, may be quoted on the opposite side of

the question ; among others, that of Leibnitz, un-

questionably one of the first names in modern philo-

sophy. But, on this point, the mind of Leibnitz

was not altogether unwarped ; for he appears to

have early contracted a partiality, not only for scho-

lastic learning, but for the projects of some of the

schoolmen to reduce, by means of technical aids, the

exercise of the discursive faculty to a sort of mecha-

nical operation ;—a partiality which could not fail

to be cherished by that strong bias towards synthe-

tical reasoning from abstract maxims, which charac-

terizes all his philosophical speculations. It must

be remembered, too, that he lived at a period when

logical address was still regarded in Germany as an

indispensable accomplishment to all whose taste led

them to the cultivation of letters or of science. Nor

Sect, 3. OF THE HUMAN TVIIND. 311

was this all accomplisliment of easy acquisition ; re-

quiring, as it must have done, for its attainment, a

long course of laborious study, and, for its successful

display, a more than ordinary share of acuteness,

promptitude, and invention. To all which it may

be added, that while it remained 'in vogue, it must

have been peculiarly flattering to the vanity and self-

love of the possessor ; securing to him, in every

contest with the comparatively unskilful, an inflillible

triumph. These considerations (combined with that

attachment to the study of jurisprudence which he

retained through life) may, I think, go far to ac-

count for the disposition which Leibnitz sometimes

shews to magnify a little toomuch the value of this art.

It is, besides, extremely worthy of remark, with re-

spect to this eminent man, within what narrow li-

mits he circumscribes the province of the school

logic, notwithstanding the favourable terms in which

he occasionally speaks of it. The following passage

in one of his letters is particularly deserving of at-

tention, as it confines the utility of syllogism to

those controversies alone which are carried on in

writing, and contains an explicit acknowledgment,

that, in extemporaneous discussions, the use of it is

equally nugatory and impracticable.

" I have myself experienced the great utility of

" the forms of logic in bringing -controversies to an

** end ; and wonder how it has happened, that they

<' should have been so often applied to disputes

" where no issue was to be expected, while their

** real use has been altogether overlooked. In an

** argument which is carried on viva voce, it is

5V2 ELEMENTS OF THE PHILOSOPHY Chap. III.

" scarcely possible that the Jbrms should continue

"to be rigorously observed ; not only on account

" of the tediousness of the process, but chiefly from

" the difficulty of retaining distinctly in the me-" mory all the different links of a long chain. Ac-" cordingly, it commonly happens, that after one*' prosyllogism, the disputants betake themselves to

" a freer mode of conference. But if, in a contro-

" versy carried on in writing, the legitimate forms

*' were strictly observed, it would neither be diffi-

" cult nor disagreeable, by a mutual exchange of

" syllogisms and answers, to keep up the contest,*

*' till either the point to be proved was completely

" established, or the disputant had nothing farther

*' to allege in support of it. For the introduction,

" however, of this into practice, many rules remain

" to be prescribed ; the greater part of which are to

" be collected from the practice of lawyers."!

This concession, from so consummate a judge, I

consider as of great consequence in the present ar-

gument. For my own part, if I were called on to

plead the cause of the school logic, I should cer-

tainly choose to defend, as the more tenable of the

two posts, that which Leibnitz has voluntarily aban-

doned. Much might, I think, on this ground be

plausibly alleged in its favour, in consequence of its

obvious tendency to cultivate that invaluable talent

* The words in the original arc—" non ingratum nee difficile

" foret, mitlendo remittendoquc syllogismos ct responsioncs tam-

" diu redprocare serram, donee vol confectum sit quod proban-

*' dum erat, vel nihil ultra habeat quod afferat argumentator,"

r Leibnitz. Op. Tom. VI. p. 72. Edit. Dutens.


to a disputant, which Aristotle has so significantly

expressed by the word a-yîrota ;*—a talent of

which the utility cannot be so forcibly pictured, as

in the lively and graphical description given by

Johnson, of the inconveniences with which the want

of it is attended.

" There are men whose powers operate only at

" leisure and in retirement, and whose intellectual

*' vigour deserts them in conversation ; whom merri-

^* ment confuses, and objection disconcerts ; whose

" bashfulness restrains their exertion, and suffers

** them not to speak till the time of speaking is

" past ; or whose attention to their own character

" makes them unwilling to utter at hazard what has

" not been considered, and cannot be recalled." t

The tendency, however, of scholastic disputations

to cure these defects, it must not be forgotten, be-

longs to them only in common with all other habits

of extemporaneous debate ; and the question still

recurs. Whether it would not be wiser to look for

* Aristotle's definition of ay^mia turns upon one only of the

many advantages which presence ofmind bestows, in the manage-

ment of a vivd voce dispute. "^HS' wyyjma. sgrtv ivcro-xjoi. ng iv

affxsrrrw XS'^^V"^^ fJîdov. (Sagacitas est bona qusedam medii con-

jectatio brevissimo tempore.) Analyt. Post, Lib. i. cap. 34. I

use the word, upon this occasion, in that extensive and obvious

sense which its etymology suggests, and in which the correspond-

ing Latin phrase is employed by Quinctilian. " In Altercatione

'* opus est imprimis ingenio veloci ac mobili, animo prcesenti et

" acri. Non enim cogiland urn, sed dicendum statim est,"

Quinct. Lib. vi. cap. 4.

t Life of Dryden.'

314 LLEMEXTS OF THE PHILOSOPHY Chap. III.

the remedy, in exercises more analogous to tlie i-eal

business of life ?

After having said so much in disparagement of

the art of syllogizing, I feel it incumbent on me to

add,, that I would not be understood to represent a

general acquaintance with it as an attainment of no

ralue, even in these times. Tlie technical language

connected with it is now so incorporated with all the

higher departments of learning, that, independent-

ly of any consideration of its practical applications,

some knowledge of its peculiar phraseology may be

regarded as an indispensable preparation both for

scientific and for literary pursuits.* To the philo..

* It was with great pleasure I read the concluding paragraph

of the introduction prefixed to a Compend of .Logic, sanctioned

by so learned a body as the University of Dublin.

" Utrum haecce ars per se rcvera aliquem prasstet usum, qui-

*' dam dubitavere. Quoniam vero in Authorum insigniorum

*' script's, saepe occurant termini Logici, hos terminos explica-

** tos habere, ideoque et ipsius arlis partes praecipuas, omnino

" necessarium videtur. Haec itaque in sequenti corapendio efG,

" cere est propositum."

(Artis Logic£e Compendium. In usum Juventutis Collegii

Dubliniensis.)

The arrangement of this department of academical stud)-, pro-

posed by M. Prevost of Geneva, seems to be very judiciously

and happily imagined.

" Diatectkam, quje linguse philosophiCcE usum tradit, seorsim

" doccre : et logicam, quae rationis analysin instituit, ab omni de

*' verbis disputatione sojungcre visum est.

" Logicam autem in trcs partes di vidimus: deveritate, de errore,

" de methodo: ut hsec mentis medicina, ad instar medicinoe cor-

" poris, exhibeat ordine statum naturalem, morbos, curationem."

See the preface to a short but masterly tract De Probabilitatc,

printed at Geneva in 179^'


sopher, it must ever remain a subject of speculation

peculiarly interesting, as one of the most singular

facts in tlie history of the Human Understanding.

The ingenuity and subtlety of the invention, and

the comprehensive reach of thought displayed in the

systematical execution of so vast a design, form a

proud and imperishable monument to the powers of

Aristotle's mind, and leave us only to regret, that

they were wasted upon objects of so little utility.

In no point of view, however, does this extraordi-

nary man appear to rise so far above the ordinary

level of the species, as when we consider the do-

minion which he exercised, during so long a suc-

cession of ages, over the opinions of the most civi-

lized nations. Of this dominion the basis was chiefly

laid in the syllogistic theory, and in the preparatory

books on the Categories and on Interpretation ; a

part of his works to which he was more indebted

for his authority in the schools than to all the rest

put together. Is it extravagant to conjecture, that

Aristotle himself foresaw this ; and that, knowing

liow prone the learned are to admire what they

do not comprehend, and to pride themselves on the

possession of a mystical jargon, unintelligible to the

nmltitude, he resolved to adapt himself to their taste

in those treatises which were destined to serve, in the

first instcmce, as the foundation of his fame? If such

was really his idea, the event has shewn how soundly

he judged of human nature, in this grand experi-

ment upon its weakness and ductility.*

* The following historical sketch from Ludoticus Vires may

serve to shew that the foregoing supposition is not altogether

316 ELEMENTS OF THE PHILOSOPHY Chap. HI,

That Aristotle'sworks have of late fallen into gene-

ral neglect^ is a common subject of complaint arriong

his idolaters. It would be nearer the truth to say,

that the number of Aristotle's rational and enliffhten-

ed admirers was never so great as at the present mo-

ment. In the same proportion in which his logic

has lost its credit, his ethics, his politics, his poetics,

his rhetoric, and his natural history, have risen in

gratuitous. " A temporibus Platonis et Ariototelis usque ad

" Alexandrum Aphrodiseum, qui vixit Severo et ejus filiis Prin-

" cipibus, Arlstoteles nominabatur magis, quain vel Icgebatur a

' doctis vel intelligebatur. Primus ille aggressus eum enarrare,

" et adjuvit studia multorum et ad alia in eo Philosopho quae-

" renda excitavit. Mansit tamen trebrior in manibus hominum*' et notior Plato, usque ad scholas in Gallia et Italia publice con-

" stitutas, id est, quamdiu Graeca et Latina lingua viguerunt.

" Postea vero quam theatricae coeperunt esse disciplinae, omnis-

" que earum fructus existimatus est, posse disputando fucum

" facere, et os obturarc, et pulverem ob oculos jacere, idque im-

" peritissima peritia, et nominibus ad, lubitura confictis, accomo-

" datiores ad rem visi sunt libri logici Aristotelis et physici, re-

" lictis permultis prcEclaris ejus operibus: Platone vero, et quod ab

" eis non inlcllegeretur, quanivis multo minus Aristoteles, et quod

" artificium videretur docero, nc nominato quidem ; non quod

" minorcm aut ineruditiorem puLcm Platone Aristotelem, sod

" quod ferendum non est, Platonem sanctissimum philosophum

" prccteriri, et Aristotelem ita legi, ut meliorc rcjecta parte, quae

" retinetur id cogatur loqui, quod ipsi Jubent."—Lndovic. Vives

de Civ. Dei, L. viii. c. 10.

A remark similar to this is made by Baylc. " Ce qui doit

" etonner le plus les hommes sages, c'est que les professeurs se

*' soicnt si furieusemeiit cntelez des h3'potheses philosopiiiques

" d'Aristote. Si I'on avoit eu cette prevention pour sa poetique,

" et pour sa rhetorique, il y auroit nioins de sujet de s'etonner;

" mais, on s'est cntete du plus foible de ses ouvrages, je veux

• dire, de sa logique et de sa physique."-—Bsyle, Art. Aristotc

Sect. 3. *^P THE HUMAN MIND. 317

the public estimation. No similar triumph of genius

is recorded in the Annals of Philosophy :—To sub-

jugate, for so many centuries, the minds of men, by

furnishing employment (unproductive as it was) to

their intellectual faculties, at a time when the low

state of experimental knowledge did not supply

more substantial materials for their reasonings ;

—

and afterwards, when at the distance of two thou-

sand years, the light of true science began to dawn,

to contribute so large a share to its growing splen^

dour.

In the course of the foregoing animadversions on

the syllogistic theoiy, I have proceeded on the sup-

position, that the whole glory of the invention be-

longs to Aristotle. It is proper, however, before

dismissing the subject, to take some notice of the

doubts which have been suggested upon this head,

in consequence of the lights recently thrown on the

remains of ancient science still existing in the Easti

Father Pons, a Jesuit missionary, was (I believe) the

first person who communicated to the learned of

Europe the very interesting fact, that the use of

the syllogism is, at this day, familiarly known to the

Bramins of India;* but this information does not

seem to have attracted much attention in England,

till it was corroborated by the indisputable testi-

mony of Sir William Jones, in his third discourse

to the Asiatic Society.! *' It will be sufficient," he

observes, " in this dissertation to assume, what

* Lettres Edifiantes et Curicuses,Tome XX\'I. (eld edition.)

—

Tome XIV. edit, of 17S1. Tiie Iclttr is dated 1740,

f Delivered in 178^.

31S ELEMENTS OP THE rHILOSOPHY Chap. HI.

" might be proved beyond controversy, that we« now live among the adorers of those very deities

*' who were worshipped under different names in

" old Greece and Italy, and among the professors

'* of those philosophical tenets, which the Ionic and*' Attic writers illustrated with all the beauties of

*' their melodious language. On one hand we see

" the trident of Neptune, the eagle of Jupiter, the

^' satyrs of Bacchus, the bow of Cupid, and the

" chariot of the sun ; on the other, we hear the

" cymbals of Rhea, the songs of the Muses, and*' the pastoral tales of Apollo Nomius. In more re-

" tired scenes, in groves, and in seminaries of learn-

" ing, we may perceive the Brahmans and the Ser^-

** manes mentioned by Clemens, disputing in the

*^forms of logic, or discoursing on the vanity of

" human enjoyments, on the immortality of the

** soul, her emanation from the eternal mind, her

" debasement, wanderings, and final union with her

" source. The six philosophical schools, whose prin-

" ciples are explained in the Dersana Sastra, com-

" prise all the metaphysics of the old academy, the

" Stoa and tlie Lyceum j nor is it possible to rea<J

" the Vedanta, or the many fine compositions in

" illustration of it, without, believing that Pytha-

" goras and Plato derived their sublime theories from

*' the same source with the sages of India." *

* Works of Sir William Jones, Vol. I. p. 28.

In the same discourse, we are informed, that " the Hindoos

*' have numerous works on grammar, logic, rhetoric, music,

" which are extant and accessible." An examinatioa of these

is certiiinly an object of literary curiosity, highly deserving of

farther attention.


111 a subsequent discourse, the same author men-

tions " a tradition, which prevailed, according to

** the well-informed author of the Dabistdn, in the

" Paiydby and in several Persian provinces, that,

" among other Indian curiosities, which Callisthe-

*' nes transmitted to his uncle, was a technical sys'

** tern of logic, which the Brahmans had communi-

" cated to the inquisitive Greek, and which the

*' Mohammedan writer supposes to have been the

" ground-work of the famous Aristotelian method.** If this be true," continues Sir W. Jones,—and

none will dispute the justness of his remark, " it is

*' one of the most interesting facts that I have met" with in Asia." *

Of the soundness of the opinion concerning the

origin of the Greek philosophy, to which these quo-

tations give the sanction of an authority so truly re-

spectable, our stock of facts is as yet too scanty to

enable us to form a competent judgment. Some

may perhaps think, that the knowledge of the Aris-

totelian logic which exists in India, may be suffici-

ently accounted for by the Mohammedan conquests

;

and by the veneration in which Aristotle was held,

from a very early period, by the followers of the pro-

phet, t On the other hand, it must be acknow-

* Eleventh discourse, delivered in 179-1-

t " La philosophie Peripatetique s'est telleinent etablie par

" tout, qu'on n'en lit plus d'autrepar toutes les universitez Ciire-

*' tiennes. Celles memes, qui sont contraintes de recevoir les

" impostures de Mahomet, n'enseigncnt les sciences que confor-

*' mfement aux principes du Lycee, auxquels ils s'attachent si

" fort, qu'Averroes,- Alfarabius, Albumassar, et assez d'autres

320 ELEMENTS OF THE PHILOSOPHY Chap. HI.

ledged, that this part of Aristotle's work contains

some intrinsic evidence of aid borrowed from a more

ancient school. Besides that imposing appearance

which it exhibits of systematical completeness in its

innumerable details ; and which we can scarcely sup-

pose that it could have received from the original in-

ventor of the art, there is a want of harmony or uni-

ty in some of its fundamental principles, which seems

to betray a combination of different and of discord-

ant theories. I allude more particularly to the

view which it gives of the nature of science and of

demonstration, compared with Aristotle's well-

" philosophes Arabes se sont souvent eloignes des sentiments de

'* leur prophete, pour ne pas contredire ceux d'Aristote, que les

'^ Turcs out en leur idiome Turquesque et en Arabe, comme'" Belon le rapporle."

—

La Motte Ic Vayer ; quoted by Bayle,

Art. Aristote.

" L'Auteur, dont j'eraprunte ces paroles, dit dans un autre

" volume, que, selon la relation d'Olearius, les Perses ont toutes

" les oeuvres d'Aristote, cxpliquees par beaucoup de commen-" taires Arabes. ' Bergeron (dit il) remarque, dans son Traite

" des Tartares, qu'ils possedent les livres d'Aristote, traduits en

" leur langue, enseignant, avec autant de soumission qu'on pent

" faire ici, sa doctrine a Samarcand, universite du Grand Mogol,

" et a present ville capitalc du Roj'aunie d'Usbec' "

In the 8th volume of the Asiatic Researches, there is a paper

by Dr Balfour, containing some curious extracts (accompanied

with an English version) from a Persian translation of an Ara-

bic Treatise, entitled the " Essence of Logic." In the introduc-

tion to these extracts, Dr Balfour mentions it as an indisputable

fact, that " the system of logic, generally ascribed to Aristotle,

" constitutes, at this time, the logic ofall the nations of Asia ivko

^' profess the Mahometan faith ;" and it seems to have been

with a view of rendering this fact still more palpable to common

readers, that the author has taken the trouble to translate,

Sect. 3. O^ THE HUMAN MIND. 651

known opinions concerning the natural progress of

the mind in the acquisition of knowledge. That

the author of the Organon was fully aware of an in-

congruity so obvious, there can be little doubt ; and

it was not improbably with a view to disguise or to

conceal it, that he was induced to avoid, as much

as possible, every reference to examples ; and to

adopt that abstract and symbolical language, which

might divert the attention from the inanity of his de-

monstrations, by occupying it in a perpetual effort

to unriddle the terms in which they are expressed.

Nor does there seem to be anything in these sug-

gestions (which I hazard with much diffidence) in-

consistent with Aristotle's own statement, in the con-

cluding chapter of the book of Sophisms. This

chapter has indeed (as far as I know) been univer-

sally understood as advancing a claim to the whole

art of syllogism ;* but I must acknowledge, that it

appears to me to admit of a veiy fair construction,

through the medium of the Persian, the Arabic original ; from

which language the knowledge of Aristotle's logic, possessed bj-

the orientals, is supposed to have been derived.

* " The conclusion of this treatise," the book of Sophisms,

" ought not to be overlooked : it manifestly relates, not to the

" present treatise only, but also to the whole Analytics and To-

" pics of the author."

—

Reid's Analysis^ &c. Chap, v. Sect. iii.

If I were satisfied that this observation is just, I should think

that nothing short of the most irresistible evidence could be rea-

sonably opposed to the direct assertion of Aristotle. It is quite

inconceivable, that he should have wilfully concealed or misre-

presented the truth, at a period when there could not fail to be

many philosophers in Greece, both able and willing to expose

the deception,

VOL. II. 5:

322 ELEMENTS OF THE PHILOSOPHY Chap. Ill*

without supposing the claim to comprehend all the

doctrines delivered in the books of Analytics. In

support of this idea, it may he remarked, that while

Aristotle strongly contrasts the dialectical art, as

tauglit in the preceding treatise, with the art of dis-

2mtatio7i as previously practised in Greece, he does

not make the slightest reference to the distinction

between demonstrative and dialectical syllogisms, or

to those doctrines with respect to demonstration and

science, which accord so ill with the general spirit of

his philosophy. It does not seem, therefore, to be a

very unreasonable supposition, that to these doc-

trines fwith which, for many reasons, he might judge

it expedient to incorporate his own inventions and

innovations) he only gave that systematical and

technical form, which, by its peculiar phraseology

and other imposing appendages, was calculated at

once to veil their imperfections, and to gratify the

vanity of those who should make them objects of

study. It Is surely not impossible, that the syllogis-

tic theory may have existed as a subject of abstract

speculation, long before any attempt was made to in-

troduce the syllogism into the schools as a weapon of

controversy, or to prescribe rules for the skilful and

scientific management of a viva voce dispute.

It Is true that Aristotle's language, upon this oc-

casion, is somewhat loose and equivocal ; but it must

be remembered, that It was addressed to his con-

temporaries, who were perfectly acquainted with the

real extent of his merits as an inventor ; and to

whom, accordingly, it was not necessary to state his

pretensions in terms more definite and explicit.


I shall only add, that this conjecture (supposing

it for a moment to be sanctioned by the judgment of

the learned) would still leave Aristotle in complete

possession of by far the most ingenious and practical

part of the scholastic logic ; * while, at the same

time,—should future researches verify the suspicions

of Sir William Jones and others, that the first rudi-

ments of the art were imported into Greece from

the East,—it would contribute to vindicate his cha-

racter against that charge of plagiarism, and of un-

fairness towards his predecessors, which has been ad-

mitted even by some who speak with the most un-

bounded reverence of his intellectual endowments.

* This was plainly the opinion of Cicero :" In hac arte," he

observes, speaking of the dialectical art, as it was cultivated by

the Stoics,—" in hac arte, si modo est hcsc ars, nullum est pra--

" ceptum quomodo verum inveniatur, sed tantum est quomodo" judicetur."—And in a few sentences after, " Quare istacn ar-

" tern totam dimittamus, quae in excogitandis argumentis muta

"nimium est, in judicandis nimium loquax." (De Orat. Lib.

ii. 86, 870 The first sentence is literally applicable to the doc-

trine of syllogism considered theoretically : the second contrasts

the inutility of this doctrine with the importance of such subjf^cts

as are treated of in Aristotle's Topics.

Whether Cicero and Quinctilian did not overrate the advan-

tages to be derived from the study of the Luci as an organ of in-

vention, is a question altogether foreign to our present inquiries,

That it was admirably adapted for those argumentative and rhe •

torical displays which were so highly valued in ancient times,

there can be no doubt, after what these great masters of oratory

have written on the subject ; but it does not follow, that, in the

present state of society, it would reward the labours of those wlio

wish to cultivate either the eloquence of the bar, or that which

leadfi to distinction in our popular assemblies.


" From the logic of Aristotle, I now proceed to that

of Lord Bacon ; a logic which professes to guide us

systematically in investigating the laws of nature,

and in applying the knowledge thus acquired to the

enlargement of human power, and the augmentation

of human happiness.

Of some of the fundamental rules by which this

mode of philosophising is more peculiarly distin-

guished, I intend to treat at considerable length ;—directing my attention chiefly to such questions as

are connected with the theory of our intellectual fa-

culties. Jn this point of view, the author has left

much to be supplied by his successors ; the bent of

his own genius having fortunately determined him

rather to seize, by a sort of intuitive penetration,

great practical results, than to indulge a compara-

tively sterile curiosity, by remounting to the first

sources of experimental knowledge in the principles

and laws of the human frame. It is to this humbler

task that I propose to confine myself in the sequel.

To follow him through the details of his Method,

would be inconsistent with the nature of my present

undertaking.

Sect. 1. OF THE HUMAN MIND. 3^5

CHAPTER FOURTH.

©F THE METHOD OF INQUIRY POINTED OUT IN THE

EXPERIMENTAL OR INDUCTIVE LOGIC.

Section I.

Mistakes of the Ancients concerning the proper ob-

ject ofPhilosophy.—Ideas ofBacon on the same

sulyect,—Inductive Reasoning.—Analysis and

Synthesis.—Essential difference betwee?i Legiti-

mate and Hypothetical Theories,

1 HAVE had occasion to observe more than once, in

the course of tlie foregoing speculations, that the

'

object of physical science is not to trace necessary

connections, but to ascertain constant conjunctions j

not to investigate the nature of those efficient causes

on which the phenomena of the universe ultimately

depend, but to examine with accuracy what the phe-

nomena are, and what the general laws by which

they are regulated.

In order to save repetitions, I here beg leave to

refer to some observations on this subject in the first

volume. I request more particularly the reader's

3^6 ELEMENTS OF THE PHILOSOPHY Chap. IV.

attention to wliat I have said, in the second section

of the first chapter, on the distinction between phi/-

sical and efficient causes ; and on the origin of that

bias of the imagination, which leads us to confound

them under one common name. That, when we

see two events constantly conjoined as antecedent

and consequent, our natural apprehensions dispose

us to associate the idea of causation or efficiency with

the former, and to ascribe to it that power or ener-

gy by which the change was produced, is a fact ob-

vious and unquestionable ; and hence it is, that in

all languages, the series of physical causes and ef-

fects is metaphorically likened to a chain, the links

of which are supposed to be indissolubly and neces-

sarily connected. The slightest reflection, at the

same time, must satisfy us that these apprehensions

are inconsistent, and even absurd ; our knowledge

of physical events reaching no farther than to the

laws which regulate their succession ; and the words

pou'er and energy expressing attributes not of Mat-

ter but of Mind. It is by a natural bias or associa-

tion somewhat similar (as I have remarked in the

section above-mentioned) that we connect our sensa-

tions of colour, with the primary qualities of body. *

* Were it not for this bias of the imagination to identify effi-

cient with physical causes, the attention would be continually

diverted from the necessary business of life, and the useful exer-

cise of our faculties suspended, in a fruitless astonishment at

that hid(l( n machinery, over which nature has drawn an impe-

netrable veil. To prevent this inconvenient distraction of thought,

a"farther provision is made in that gradual and imperceptible

process by which the changes in the state of the Universe are, in

Sect. 1. OV THE HUMAN MIND. 3^7

This idea of the oI)ject of physical science (whicli

may be justly regarded as the ground-work of

Bacon's Novum Organon) differs essentially from

that which was entertained by the ancients ; accord-

ing to whom, " Philosophy is the science of causes."

If, indeed, by causes they had meant merely the

constant forerunners or antecedents of events, the

definition would have coincided nearly with the

statement which I have given. But it is evident,

that by causes they meant such antecedents as were

7iecessarily connected with the effects, and from a

knowledge of which the effects might be foreseen

and demonstrated : And it was owing to this con-

fusion between the proper objects of physics and of

metaphysics, that, neglecting the observation of facts

exposed to the examination of their senses, they vain-

ly attempted, by synthetical reasoning, to deduce,

as necessary consequences from their supposed

causes, the phenomena and laws of nature.

—

" Causa ea est," says Cicero, " quae id efficit cu-

" jus est causa. Non sic causa intelligi debet, ut

" quod cuique antecfidat, id ei causa sit ; sed quod

general, accomplished. If an animal or a vegetable were brought

into being before our eyes, in an instant of time,— the event would

not be in itself more wonderful than their slow growth to maturi-

ty from an embryo, or from a seed. But, on the former suppo-

sition, there is no man who would not perceive and acknowledge

the immediate agency of an intelligent cause ; whereas, accord-

ing to the actual order of things, the effect steals so insensibly on

the observation, that it excites little or no curiosity, excepting

in those who possess a sufficient degree of reflection to contrast

the present state of the objects around them, with their first ori-

gin, and with the progressive stages of their existence.

328 ELEMENTS OF THE PHILOSOPHY Chap. IV.

" cuique efficienter antecedat.—Itaque dicebat Car-

" neades ne Apollinem quidem posse dicere futura,

** nisi ea, quorum causas natura ita contineret, ut

** ea fieri necesse esset. Causis enim efficientibus

" quamque rem cognitis, posse denique sciri quid

" futurum esset." *

From this disposition to confound efficient with

physical causes, may be traced the greater part of

the theories recorded in the history of philosophy.

* De Fato, 48, 49. The language of Aristotle is equally

explicit. Er/craiTiJeM Ot oio.UjiQa sxaffrov acTAwg, aXXa ^»j rov rfo«

(piSrrAov Tôjrov, rov xara ffu/XjSs/Sjjzog, orav rrjv ratriav oiu'Mida yivug-

xnv, di i]v TO 'TTây/Mo, idriv, on iyMva atria, iSri, jo firj svSsp^gra/ rsr

aXXug s-îiv. "• S;iri autem putamus uiiamquamque rem sim-

** pliciter, non sophistico moli), id est accidenti, cum puta-

" nius causam cognoscere propter quam res est, ejus rei cau-

*' sam esse, nee posse earn aliler se habere."

—

Analyt. Poster.

Lib. i. cap. 2.

Nothing, however, can place in so strona a light Aristotle's

idea ot the connection between physical causes and effects, as

the analo;:y which he conceived it to bear to the connection be-

tween the links of a mathematical chain of reasoning. Nor is

this mode of speaking abandoned by his modern followers. '* Tof deny a first cause," says Dr Gillies. " is to deny all causation:

" to deny axioms is. for the same reason^ to deny all demonstra.

" tion." (^Vol. I. p. 108 ) And in another passage, " We know" a mathematical proposition, when we know the causes that

" make it true. In demonstration, the premises are the causes

*' of the conclusion, and therefore prior to it. We cannot, there*

" fore, demonstnte things in a circle, supporting the premises by" the conclusion ; because this would be to suppose, that the one

" proposition could be both prior and posterior to the other.'*

(Ibid. p. g6.) (Can one mathematical theorem be said to be prior

to another in any other sense, than in respect of the order in

which thoy are first presented to our knowledge ?)

S*Ct. 1. OF THE HUMAy MIVD. S29

It is this which has given rise to the attempts, both

in ancient and modern times, to account ibr all the

phenomena of moving bodies by means of impulse;*

and It is this also which has suggested the simpler

expedient of explaining them by the agency of

minds united with the particles, of matter, t As the

* See Philosophy of the Human Mind, Vol. 1 Chap. i. sect,2.

With re^'pect tn the connection betwetn mpuise and motion,

I have the misfortune to difTer from my very learned and highly

respected friend M. Prevost of Geneva ; whose opii:iuns on this

point may be collected from the two following sentences. " La

" cause differe du simple signe precurseur, par sa force, ou son

" energie productive.—L'lmpulsion est un phenomena si com-*' mun, soumis h, des lois si bien discutees, et si uuiverselles, que

** toule cause qui s'y reduit semble former une classe eminente,

*' et meriter seule !e nom d'Age7it."—Essais de Philosophies

Tome II. pp. 174, 175.

I have read with great attention all that M. Prevost has so in*

geniousiy urged in vindication of the theory of his illustrious

countryman Le Sage ; but without experiencing that conviction

which I have in general received from his reasonings. The ar-

guments of Locke and Ilume on the other side of the question,

appear to my judgment, the longer 1 reflect on them, the more

irresistible ; not to mention the powerful support which they de-

rive from the subsequent speculations of Boscovich.—See Locke's

Essay, B. IL Chap. 23. § 28, 29. and Hume's Essay on Necessary

Connexion, Part I.

Jn employing the word misfortune, on this occasion, I have no

wish to pay an unmeaning compliment; but merely to express

the paniful diffidence which I always feel in my own conclusions,

when they happen to be at variance with those of a writer equally

distinguished by the depth and by the candour of his philoso-

phical researches.

For some additional illustrations of M. Prevost's opinion on this

subject, see Appendix,

f To this last class of theories may also be referred the expla*

330 ELEMENTS OP THE PHILOSOPHY Chap. IV.

communication of motion by apparent impulse, and

our own power to produce motion by a volition of

the mind, are two facts, of which, from our earliest

infancy, we have every moment had experience

;

we are apt to fancy that we understand perfectly

the ne^'us by which cause and effect are here ne-

cessarily conjoined ; and it requires a good deal of

reflection to satisfy us that, in both cases, we are as

completely in the dark, as in our guesses concern-

ing the ultimate causes of magnetism or of gravita-

tion. The dreams of the Pythagorean school, with

respect to analogies or harmonies between the con-

stitution of the universe, and the mathematical pro-

perties of figures and of numbers, were suggested

by the same idea of necessary connections existing

among physical phenomena, analogous to those

which link together the theorems of geometry or

of arithmetic ; and by the same fruitless hope of

penetrating, by abstract and synthetical reasoning,

into the mysterious processes of nature.

Beside this universal and irresistible bias of the

imagination, there were some peculiarities in the

genius and scientific taste of Aristotle, which gave

birth to various errors calculated to mislead his fol-

lowers in their physical inquiries. Among these

errors may be mentioned, as one of the most im-

portant, the distinction of causes (introduced by

him) into the efficient, the material, the formal, and

the final j—a distinction which, as Dr Reid justly

nations of physical phenomena by such causes as sympathies, an-

tipathies, Nature's horror cf a void, &ic. and other phrases bor-

rowed by analogy from the attributes of animated beings.


observes, amounts only (like many other of Ari-

stotle's) to an explanation of the different meanings

of an ambiguous word ; and which, tlierefore, was

fitter for a dictionary of the Greek language, than

for a philosophical treatise. * Of the eifcct of this

enumeration of causes in distracting the attention,

some idea may be formed, when it is recollected,

that, according to Aristotle, it is the business of the

philosopher to reason demonstratively from all the

four, t

The same predilection of Aristotle for logical, or

rather verbal subtilties, encouraged, for many ages,

that passion for fanciful and frivolous distinctions,

which is so adverse to the useful exercise of the in-

tellectual powers. Of its tendency to check the

progress of physical knowledge, the reader will be

enabled to judge for himself, by perusing the iGtli

and lyth chapters of Mr Harris's Philosophical Ar-

rangements ; which chapters contain a very elabo-

rate and not inelegant view of what the author is

pleased to call the ancient Theory of Motion. Alater writer of the same school has even gone so far

as to assert, that it is such researches alone which

merit the title of the Philosophy of Motion ; and

that the conclusions of Galileo and of Newton,

—

amounting (as they unquestionably do) to nothing

more than a classification and generalization of

facts,—deserve no higher an appellation than that

of Natural History. X

* Analysis of Aristotle's Logic. Clmp. ii. sect. 3.

f Nat. Auscult. Lib. ii. cap. 7.

J Ancient Metaphysics, ;wwi?«.—The censure bestowed on


In contrasting, as I have now done, the spirit of

Bacon's mode of philosophizing with that of the an-

cients, I do not mean to extol his own notions con-

cerning the relation of cause and effect in physics,

as peculiarly correct and consistent. On the con-

trary, it seems to me evident, that he was led to his

logical conclusions, not by any metaphysical analysis

of his ideas, but by a conviction, founded on a review

of the labours of his predecessors, that the plan of

inquiry by which they had been guided must have

been erroneous. If he had perceived as clearly as

Barrow, Berkeley, Hume, and many others, have

done since his time, * that there is not a single in-

stance in which we are able to trace a necessary con-

nection between two successive events, or to explain

Aristotle's Physics, by the authors of the French Treatise of

Logic, entitled UArt de Penser, is judicious and discrimi-

nating. " Le principal defaut qu'on y peut trouver, n'est pas

" qu'elle soit fausse, mais c'est au contraire qu'elle est trop

" vraie, et qu'elle ne nous apprend que des choses qu'il est

" impossible d'ignorer."

* In alluding to the relation between cause and effect, Ba-

con sometimes indulges his fancy in adopting metaphorical and

popular expressions. " Namque in limine Philosophiae, cum" secundai causae, tanquam sensibus proximae, ingerant se menti

" humanse, mensque ipsa in illis hasreat, atque commoretur,

'* oblivio primae causae obrepere possit. Sin quis ulterius per-

'* gat, causarumque dependentiam, serieniy et concatenationem, at-

" que opera providcntiae intucatur, tunc secundum poetarum

" mythologiam, facile credet, summum naturalis catena: annulum

" pedi solii Jovis affigi." (De Aug. Scient. Lib. i.) This is very

nearly the language of Seneca. " Cum fatum nihil aliud sit

" quam series irnplexa cmisarum, ille est prima omnium causa ex

'< qua cetcrae pendent."


in what manner the one follows from the other as

an infallible consequence, he would have been na-

turally led to state his principles in a form far more

concise and methodical, and to lay aside much of

that scholastic jargon by which his meaning is occa-

sionally obscured. Notwithstanding, however, this

vagueness and indistinctness in his language, his

comprehensive and penetrating understanding, en-

lightened by a discriminating survey of the fruitless

inquiries of former ages, enabled him to describe, in

the strongest and happiest terms, the nature, the ob-

ject, and the limits of philosophical investigation.

The most valuable part of his works, at the same

time, consists, perhaps, in his reflections on the er-

rors of his predecessors ; and on the various causes

which have retarded the progress of the sciences and

the improvement of the human mind. That he

should have executed, with complete success, a sys-

tem of logical precepts for the prosecution of experi-

mental inquiries, at a period when these were, for

the first time, beginning to engage the attention of

the curious, was altogether impossible ; and yet in

his attempt towards this undertaking, he has display-

ed a reach of thought and a justness of anticipation,

which, when compared with the discoveries of the

In other instances he speaks (and, in my opinion, much more

philosophically) of the " opus quod operatur Deus a primordio

" usque ad finem ;" a branch of knowledge which he expressly de-

scribes as placed beyond the examination of the human faculties.

But this speculation, although the most interesting that can em-

ploy our thoughts, has no immediate connection with the logic

•f physical science.—See Note (N.)

334f ELEMENTS OF THE PHILOSOPHY Chap. IV.

two sur'êeding centuries, seem frequently to partake

of the nature of propliecy. ** Prout Physica majo-

" ra indies incrementa capiet, et nova axiomata

" educet, eo mathematical nova opera in multis in-

" digebit, et plures demum fient mathematicae

" mixtae.*' * Had he foreseen all the researches of

the Newtonian school, his language could not have

been more precise or more decided.

" Bacon," it has been observed byMr Hume, " was

" ignorant of geometry ; and only pointed out at a

" distance the road to true philosophy.'*—** As an

" author and philosopher," therefore, this historian

pronounces him, " though very estimable^ yet infe-

" rior to his contemporary Galileo, perhaps even to

" Kepler." t—The parallel is, by no means, happi-

ly imagined ; inasmuch as the individuals whom it

brings into contrast, directed their attention to pur-

suits essentially different, and were characterized by

mental powers unsusceptible of comparison. As a

* De Aug. Scient. Lib. iii. Cap. vi.

By the word Axiom, Bacon means a general principle obtained

by induction, from which we may safely procee<l to reason syn-

thetically. It is to be regretted, that he did not make choice of

a less equivocal term, as, Newton has plainly been misled by his

example, in the very illogical application of this name to the laws

of motion, and to those generaiyac/5 which serve as the basis of

our reasonings in catoptrics and dioptrics. (See pp. 43, 44, of

this volume.)

I shall take this opportunity to remark, that Newton had evi-

dently studied Bacon's writings with care ; and has followed them

(sometimes too implicitly, in his logical phraseology. Of this

remark various other proofs will occur afterwards.

t History of England. Appendix to the reign of James I.


geometer or astronomer, Bacon has certainly no

claim whatever to distinction ; nor can it even be

said, that, as an experimentalist, he has enriched

science by one important discovery : but, in just and

enlarged conceptions of the proper aim of philosophi-

cal researches, and of the means of conducting them,

how far does he rise above the level of his age ! No-

thing, indeed, can place this in so strong a light, as

the history of Kepler himself ; unquestionably one

of the most extraordinary persons who adorned that

memorable period, but deeply infected, as his writ-

ings shew, with prejudices borrowed from the most

remote antiquity. The mysterious theories of the

Pythagoreans, which I formerly mentioned, and

which professed to find in the mathematical proper-

ties of figui'es and numbers, an explanation of the

system of the universe, seem, from one of his earlier

publications, to have made a strong impression on his

imagination j* while, at an after period of life, he

* Mysterhim Cosmograpkicum, dc admirabili proportione or-

bium ccelestium deque causis coelorum numeri, magnitudinis, mo-

tuumque periodicorura genuinis et propriis, demonstratum per

quinque regiduria corpora Geometrka, 1598. Kepler informs us,

that he sent a copy of this booic to Tycho Brahe ; the subject of

whose answer he has had the candour to record. " Argumen-

" turn literarum Brahei hoc erat, ut suspensis speculationibus a

" priori descendentibus, animum potius ad observationes quas

" simul oft'crebat, considerandas adjicercm, inque iis prime gradu

" facto, posted demum ad causas ascenderem."—To this excel-

lent advice the subsequent discoveries, which have immortalized

the name of Kepler, may (in the opinion of Mr Maclaiirin) be

ascribed.

—

Account of Nexvton's Discoveries, Book I. Chap. iii.

An aphorism of Lord Bacon, concerning the relation which

SS6 ELEMENTS O? THE PHILOSOPHY Chap IV.

indulged himself in a train of thinking about the

causes of the planetary motions, approaching to the

Blathematics bears to Natural Philosophy, exhibits a singular

contrast to the aim and spirit of the Mysterium Cmmograpkicum,

" In secuuda schola Platonis, Procli et aliorum, Naturalis Philo-

" sophia infecta et corrupta fuit, per Mathenialicam; quts Phi-

** losophiam Natiiralem terminare, 7ion generare aut procreate

" debet." (Nov. Org. Lib. I. Aphor. xcvi.)—The very slen-

der knowledge of this science which Bacon probably possessed,

renders it only the more wonderful, that he should have been so

fortunate in seizing, or rather in divining, its genuine use and ap-

plication in physical researches.

The ignorance of geometry with which Mr Hume reproaches

Bacon, will not appear surprising, when it is considered, that,

sixty years after the time when he left Cambridge, mathematical

studies were scarcely known in that University. For this fact

we have the direct testimony of Dr Wallis (afterwards Astronomi-

cal Professor at Oxford), who was admitted at Emanuel College,

Cambridge, in l632 ; and who informs us, that at that time,

" IVIathematics were scarce looked upon as Academical Studies,

" but rather Mechanical ; as the business of trailers, merchants,

" seamen, carpenters, surveyors of land, and almanack-makers in

*' London."—" Among more than two hundred students in our

" College, I do not know of any two who had more than I (if so

" much), which was then but little ; and but very few in that

" whole University. For the study of Mathematics was then

" more cultivated in London than in the Universities."

(See an Account of some passages in the Life of Dr Wallis^

written by himself when he was upwards of eighty, and publish-

ed by Heariie, in his edition of Langtoft's Chronicle.)

The same writer, from whom this information is derived, lived

to see, not only the institution of the Royal Society of London,

but the illustration which the University of Cambridge derived

from the names of Barrow and of Newton ; and even survived, for

seventeen years, the publication of Newton's Principia.—That

Lord Bacon's writings contributed, more than any other single


Speculations of the late learned author of Ancient

Metaphtjsics.

*' Nego," says he, in liis Commentaries on the pla-

net Mars, " ullum motum perennem non rectum a

" Deo conditum esse pra3sidio mentali destitutum.—

" Hujus motoris manifestum est duo fore munia;

" alterum ut facultate polleat transvectandi corporis;

" alterum ut scientia pra^ditus sit inveniendi circula-

" rem limitem per illam puram auram êtheriam nul-

" lis hujusmodi regionibus distinctam."—In another

part of his work, he seriously gives it as his opinion,

that the minds of the planets must have a power of

making constant observations on the sun's apparent

diameter, that they may thereby be enabled so to re-

gulate their motions, as to describe areas proportional

to the times. " Credibile est itaque, si qua facultate

** prêditi sint motores illi observandai hujus diametri,

*' eam tanto esse argutiorem quam sunt oculi nostri,

" quanto opus ejus et perennis motio nostris turbu-

" lentis et confusis negotiis est constantior.

" An ergo binos singulis planetis tribues oculos

" Keplere ! Nequaquam. Neque est necesse. Ne-*' que enim ut moveri possiiit, pedes ipsis atque ala?

" sunt tribuendae."

From such extravagancies as these, how wide the

transition to the first sentence of the Novum Orsia-

non !" Homo Nature minister et interpres

" tantum facit et intelligit quantum de na-

" TURiE ORDINE RE VEL MENTE OBSERVAVERIT,

" NEC AMPLIUS SCIT AUT POTEST."

cause, to give this sudden impulse to science in England, it is im-

possible to doubt,

VOL. II. Y

33S ELEMENTS OF THE PHILOSOPHY Chap. IV*.

In calling man the interpreter of Nature, Bacon

had plainly the same idea of the object of physics,

which I attempted to convey, when I said, that what

are commonly called the causes of phenomena, are

only their established antecedents or signs ; and the

same analogy which this expression suggests to the

fancy, has been enlarged upon, at considerable

length, by the inventive and philosophical Bishop of

Cloyne, as the best illustration which he could give

of the doctrine in question. It would be difficult,

indeed, to select another equally apposite and lumi-

nousJand not less difficult to find an author equal-

ly qualified to avail himself of its aid. I shall make

no apology, therefore, for borrowing his words.

" There is a certain analogy, constancy, and uni-

' formity, in the phenomena or appearances of na-

' ture, which are a foundation for general rules

;

' and these are a grammar for the understanding of

' nature, or that series of effects in the visible world,

' whereby we are enabled to foresee what will come

' to pass in the natural course of things. Plotinus

' observes, in his third Ennead, that the art of pre-

' saging is, in some sort, the reading of natural let-

' ters denoting order ; and that so far forth as ana-

' logy obtains in the universe, there may be vatici-

' nation. And, in reality, he that foretels the mo-

* tions of the planets, or the effects of medicines,

' or the results of chemical or mechanical experi-

ments, may be said to do it by natural vaticination.

" We know a thing when we understand it, and

" we understand it when we can interpret or tell

" what it signifies. Strictly the sense knows no-

Sect. t. OV THE HUMAN MIND. 339

" thing. We perceive, indeed, sounds by hearing,

" and characters by sight ; but we are not, there-

*' fore, said to understand them. After the same

*' manner, the phenomena of nature are alike visible

'< to all ; but all have not alike learned the connec-

" tion of natural signs, or understand what they sig-

*' nify, or know how to vaticinate by them. There

" is no question, says Socrates in Thewteto, concern-

" ing that which is agreeable to each person, but

" concerning what will in time to come be agreeable,

" of which all men are not equally judges. He" that foreknowetli what will be, in every kind, is

" the wisest. According to Socrates, you and the

" cook may judge of a dish on the table equally well y

*' but while the dish is making, the cook can better

" foretel what will ensue from this or that manner*' of composing it. Nor is this manner of reasoning

" confined only to morals or politics, but extends al-

" so to natural science.

" As the natural connection of signs with the

*' things signified is regular and constant, it forms a

" sort of rational discourse, and is therefore the im-

" mediate effect of an intelligent cause." *

The same language, with respect to the office and

use of philosophy, has been adopted by Reid, and at

a much earlier period by Hobbes ; and it was evi-

dently by a similar train of thinking (as I already

hinted) that Bacon was led to call philosophy the in"

ierpretation ofnature.

* Siris : or a Chain of Philosophical Reflections and Inquiries

concerning the virtues of Tar-Water, §§ 252, 253, 254.

34?0 ELEMENTS OF THE PHILOSOPHY Chap. IV.

According to the doctrine now stated, the highest,

or rather the only proper object of Physics, is to as-

certain those established conjunctions of successive

events, which constitute the order of the Universe ;

to record the phenomena which it exhibits to our ob-

servations, or which it discloses to our experiments;

and to refer these phenomena to their general laws.

While we are apt to fancy, therefore (agreeably to

popular conceptions and language), that we are in-

vestigating efficient causes, we are, in reality, only

generalizing effects ; and when we advance from

discovery to discovery, we do nothing more than re-

solve our former conclusions into others still more

comprehensive. It was thus that Galileo and Tor-

ricelli proceeded in proving that all terrestrial bodies

gravitate towards the earth ; and that the apparent

levity of some of them is merely owing to the greater

gravity of the atmosphere. In establishing this im-

portant conclusion, they only generalized the law of

gravity, by reconciling with it a variety of seeming

exceptions ; but they threw no light whatever on

that mysterious power, in consequence of which all

these phenomena take place. In like manner, when

Newton shewed that the same law of gravity extendi

to the celestial spaces ; and that the power by which

the moon and planets are retained in their orbits, is

precisely similar in its effects to that which is mani-

fested in the fall of a stone,—he left the efficient

cause of gravity as much in the dark as ever, and only

generalized still farther the conclusions of his pre-

decessors. It was, indeed, the most astonishing and

sublime discovery which occurs in the history of


science ;—a discovery not of less consequence in

Natural Religion than in Natural Philosophy,—and

which at once demonstrated (in direct contradiction

to all the ancient systems) that the phenomena exhi-

bited by the heavenly bodies, are regulated by the

same laws which fall under our observation on the

surface of this globe. Still, however, it was not the

discovery of an efficient cause, but only the generali-

zation of a fact. *

From what has been said, it is sufficiently evident,

that the ultimate object which the philosopher aims

at in his researches, is precisely the same with that

which every man of plain understanding, however

uneducated, has in view, when he remarks the events

* " The laws of attraction and repulsion are to be regarded as

" laws of motion, and these only as rules or methods observed ia

" the production of natural effects, the efficient and final causes

*' whereof are not of mechanical consideration. Certainly if the

" explaining a phenomenon be to assign its proper efficient and

" final cause, it should seem the mechanical philosophers never

" explained anything; their province being only to discover the

" laws of nature ; that is, the general rules and methods of mo-

" tion ; and to account for particular phenomena, by reducing

" them under, or shewing their conformity to, such general rules,"

—Berkeley's Siris.

" The words attraction and repulsion may, in compliance with

" custom, be used where, accurately speaking, motion alone is

" meant."—" Attraction cannot produce, and in that sense ac-

" count for, the phenomena ; being itself one of the phenomena

" produced and to be accounted for."—Ibid.

For some very important as well as refined observations on

the respective provinces of physics and of metaphysics in the

theory of molion, see a Tract by Dr Berkeley, first published at

London in 1 72 1 . The title is, De Motu ; sive de Motus prin-

cipio et natura, et de causa communicationis Motuum,


which fall under his observation, in order to obtain

rules for the future regulation of his conduct. Themore knowledge of this kind we acquire, the better

can we accommodate our conduct to the established

course of things ; and the more are we enabled to

avail ourselves of natural agents as instruments for

accomplishing our purposes. It is with truth, there-

fore, that Bacon so often repeats, that " every ac-

*' cession which Man gains to his knowledge is also

*^ an accession to his power ; and extends the limits

" of his empire over the world which he inhabits.'*

The knowledge of the philosopher differs from

that information which is the fruit of common ex-

perience, not in kind, but in degree. The latter is,

in general, confined to such facts as pi'esent them-

selves spontaneously to the eye : and so beautifully

is the order of nature adapted to our wants and ne-

cessities, that while those laws in which we are most

deeply interested are obtruded on our notice from

our earliest infancy, others are more or less removed

from the immediate examination of our senses, to

stimulate curiosity, and to present a reward to in-

dustry. That a heavy body, when unsupported, will

fall downwards ; that a painful sensation would be

felt, if the skin were punctured or lacerated ; that

life might be destroyed by plunging into a river, or

by throwing one's self headlong from a precipice, are

facts as well known to the savage as to the philoso-

pher, and of which the ignorance would be equally

fatal to both. For acquiring this, and other infor-

mation of the same sort, little else is requisite than

the use of our perceptive organs : And, accordingly,


it is fiimiliar to every man, long before the period

that, in his maturer years, falls under the retrospect

of memory.

For acquiring a knowledge of facts more recon-

dite, observation and ea'periment must be employ-

ed ;* and, accordingly, the use of these media forms

one of the characteristical circumstances by which

the studies of the philosopher are distinguished from

the experience of the multitude. How much the

stock of his information must thereby be enlarged is

sufficiently manifest. By habits of scientific atten-

tion, his accuracy as an observer is improved ; and a

* To these Condorcet adds calculation. " Bacon," he ob-

serves, " has revealed the true method of studying nature, by

" employing the three instruments with which she has furnished

*' us for the discovery of her secrets,—observation, experiment,

" and calculation."

—

{Tableau Historique desprogres de VEsprit

Huinain.) In this enumeration, it appears to me that there is

a great defect, in point of logical distinctness. Calculation is

certainly not an instrument of discovery at all analogous to expe-

riment and observation : it can accomplish nothing in the study

of nature, till they have supplied the materials ; and is, indeed,

only one of the many arts by which we are enabled to give a

greater degree of accuracy to their results. The use of optical

glasses ; of the thermometer and barometer ; of time-pieces ;

and of all the various instruments of practical geometry, might,

with equal propriety, have been added to the list.

The advantages, at the same time, which Natural Philosophy

has derived, in modern times, from the arithmetical precision

thus given to scientific details, must be allowed to be immense

;

and they would be well entitled to an ample illustration in a sys-

tem of inductive logic. To those who may wish to prosecute the

subject in this view, I would beg leave to suggest the word meii'

suration as equally precise, and more comprehensive, than the

Vord calculatiorif as employed by Condo rcet.

541« ELEMENTS OF THE PHILOSOPHY Chap. IV.

precision is given to his judgment, essentially differ-

ent from the vagueness of ordinary perception : by a

combination of his own observations with those made

by others, he arrives at many conclusions unknown

to those who are prevented, by the necessary avoca-

tions of human life, from indulging the impulse of a

speculative curiosity ; while the experiments which

his ingenuity devises, enable him to place nature in

situations in which she never presents herself spon-

taneously to view, and to extort from her secrets

over which she draws a veil to the eyes of others. *

* These primary and essential organs of accurate information

•{observation and experiment), which furnish the basis to the

whole superstructure of physical science, are very clearly and

concisely described by Buscovic/i, in one of his notes on Stay's

poem, De Syste7nate Miindi. " Observationes fiunt spectando id

" quod natura per se ipsam sponte exhibet: hujusmodi sunt ob-

" servationes pcrtipentes ad astronoraiam et historiam natura-

" lem. Experimenta fiunt ponendo naturam in eas circumstan-

*' tias, in quibus debeat agdre et nobis ostendere id quod quasri-

" mus, quod pertinet ad physicani oxperimentalem. Porro et

" ferro et igni utimur, ac dissolvimus per vim compagem corpo-

" rum, potissimum in chemia, et naturam quodamraodo velut

" torquentes cogimus revelare sua secreta."

I have elsewhere remarked, that the physical discoveries of

the moderns have been chiefly owing to the skilful contrivance

and conduct of experiments ; and that this method of interrogat-

ing nature was, in a great measure, unknown to the ancients.

{Philosophical Essays, 4to, p. xxxv.) Even Aristotle himself is

acknowledged, by one of his most devoted admirers, to have con-

fined himself chiefly to observation ; and is, on this very ground,

proudly contrasted with the empirical experimentalists of the

present times, *' Aristotle," says Dr Gillies, " was contented

" with catching nature in ihe fact, without attempting, after the

" modern fashion, to put her to the torture ; and in rejecting ex-


But the observations and experiments of tlie phi-

losopher are commonly only a step towards a farther

<' periments operose, toilsome, or painful, either to their objects

" or their authors, he was justified by the habits of thinking, al-

" most universally prevalent in his age and country. Educated

" in free and martial republics, careless of wealth, because un-

" corrupted by luxury, the whole tribe of ancient Philosophers

" dedicated themselves to agreeable only and liberal pursuits,

" with too proud a disdain of arts merely useful or lucrative-

" They ranked with the first class of citizens ; and, as such, were

" not to be lightly subjected to unwholesome or disgusting em-

" ployments. To bend over a furnace, inhaling noxious steams,

" to torture animals, or to touch dead bodies, appeared to them

" operations not more misbecoming their humanity, than un-

" suitable to their dignity. For such discoveries as the heating

" and mixing of bodies ofl'ers to inquisitive curiosity, the natu-

" ralists of Greece trusted to slaves and mercenary mechanics,

" whose poverty or avarice tempted them to vvork in metals and

" minerals ; and to produce, by unwearied labour, those colour-

" ed and sculptured ornaments, those gems, rings, cups, and

" vases, and other admired but frivolous elegancies, of which

" (in the opinion of good judges of art) our boasted chemistry

" cannot produce the materials ; nor, were the materials at

*' hand, supply us with instruments fit to shape. The work-

" shops of tradesmen then revealed those mysteries which are

" now sought for in colleges and laboratories ; and useful know-

" ledge, perhaps, was not the less likely to be advanced, while

*' the arts were confined to artists only ; nor facts the more like-

" ly to be perverted, in order to support favourite theories, be-

** fore the empiric had yet assumed the name, and usurped the

** functions, of the philosopher."

—

Translation of Aristotle s

Ethics and Politics, Vol. I. p. l6l, 2d Ed.

In another passage, we are told by the same author, that " the

*' learning of Greece properly terminates m the Stagirite, by

" whom it was finally embodied into one great work ; a work

" rather impaired than improved by the labours of succeeding

" ages^' !—Ibid. p. x. of the Preface.


end. This end is, jftrst^ to resolve particular facts

into other facts more simple and comprehensive :

and, secondly, to apply these general facts (or, as

they are usually called, these laws of nature) to a

synthetical explanation of particular phenomena.

These two processes of the mind, together with that

judicious employment of observation and experiment

which they presuppose, exhaust the whole business

of philosophical investigation ; and the great object

of the rules of philosophising is, to shew in wh^t

manner they ought to be conducted.

I. For the more complete illustration of this fun-

damental doctrine, it is necessary for me to recur to

what has been already stated with respect to our ig-

Notwithstanding the length of this note, I must beg leave to

add to it a short extract from one of the aphorisms of Lord Ba»

con.—" Of the criteria for guiding our judgment among so many" different and discordant schools, there is none more to be re-

" lied on, than that which is exhibited by their fruits ; for the

*' fruits of any speculative doctrine, or the inventions which it

*' has really produced, arc, as it were, sponsors or vouchers for

*' the truths which it contains. Now, it is well known, that

*' from the philosophy of the Greeks, with its numerous deriva-

" tivc schools, hardly one experimental discovery can be collect-

'• cd which has any tendency to aid or to ameliorate the condi«

" tion of man, or which is entitled to rank with the acknow-

*' ledged principles of genuine science."—" Wherefore, as in re-

" ligion, faith is proved by its Avorks, so in philosophy, it were to

" be wished, that those theories should be accounted vain, which,

" when tried by their fruits, are barren ;—much more those,

" which, instead of grapes and olives, have produced only the

" thorns and thistles of controversy."

—

Nov. Org. Lib. i. Aph,

Ixiii,


norance of efficient causes. As we can, in no in-

stance, perceive the link by which two successive

events are connected, so as to deduce, by any rea-

soning a piiorif the one from the other as a conse-

quence or effect, it follows, that when we see an

event take place which has been preceded by a com-

bination of different circumstances, it is impossible

for human sagacity to ascertain whether the effect

is connected with all the circumstances, or only with a

pa7't of them ; and (on the latter supposition) which

of the circumstances is essential to the result, and

which are merely accidental accessories or concomi-

tants. The only way, in such a case, of coming at

the truth, is to repeat over the experiment again and

again, leaving out all the different circumstances

successively, and observing with what particular

combinations of them the effect is conjoined. If

there be no possibility of making this separation,

and if, at the same time, we wish to obtain the

same result, the only method of insur'mg success is

to combine together all the various circumstances

which were united in our former trials. It is on

this principle, that I have attempted, in a former

chapter of this work, to account for the superstitious

observances which always accompany the practice of

medicine among rude nations. These are com-

monly ascribed to the influence of imagination, and

the low state of reason in the earlier periods of so-

ciety ; but the truth is, that they are the necessaiy

and unavoidable consequences of a limited experi-

ence, and are to be corrected, not by mere force of

S48 ELEMENTS OF THE PHILOSOPHY Chap. IV.

intellect, but by a more enlarged acquaintance with

the established order of nature. *

Observations perfectly similar to those which I

made with respect to medicine are applicable to all

the other branches of philosophy. Wherever an in-

teresting change is preceded by a combination of

different circumstances, it is of importance to vary

our experiments in such a manner as to distinguish

what is essential from what is accessory ; and when

we have carried the decomposition as far as we can,

we are entitled to consider this simplest combination

of indispensable conditions, as the physical cause of

the event.

Wlien, by thus comparing a number of cases,

agreeing in some circumstances, but differing in

others, and all attended with the same result, a phi-

losopher connects, as a general law of nature, the

event with its physical cause^ he is said to proceed

according to the method of induction. This, at

least, appears to me to be the idea, which, in gene-

ral. Bacon himself annexes to the phrase ; t although

I will not venture to affirm, that he has always em-

ployed it with uniform precision. I acknowledge,

also, that it is often used by very accurate writers, to

denote the whole of that system of rules, of which

the process just mentioned forms the most essential

and characteristical part.

* Elements of the Philosophy of the Human Mind, Vol. I.

Chap. V. Part ii. sect. i.

-j- •' Inductio, 011133 ad inventionem et dcmonstrationem scientia-

" rum et allium ei it utilis, naturam separare debet, per rejectionc?

*' et exclusiones debitas," &c. &c.— jVot;. Org. Lib. i. Aph, cv.

Sect. 1. OF THE HUMAN MIND. * 349

The same word induction is employed by mathe-

maticians in a sense not altogether different. In

that general formula (for instance) known by the

name of the Binomial Theorem, having found that it

corresponds with the table of powers raised from a

Binomial root, as far as it is carried by actual mul-

tiplication, we have no scruple to conclude, that it

holds universally. Such a proof of a mathematical

theorem is called a proof by induction ;—a mode

of speaking obviously suggested by the previous ap-

plication of this term to our inferences concerning

the laws of nature. There is, at the same time,

notwithstanding the obvious analogy between the

two cases, one very essential circumstance \by which

they are discriminated ;—^that, in mathematical in-

duction, we are led to our conclusion (as I shall af-

terwards endeavour to shew), by a process ofthought,

which, although not conformable to the rules of le-

gitimate demonstration, involves, nevertheless, a lo-

gical inference of the understanding with respect to

ail universal truth or theorem ; whereas, in drawing

a general physical conclusion from particular facts,

we are guided merely by our instinctive expectation

of the continuance of the laws of nature ; an expec-

tation which, implying little, if any, exercise of the

reasoning powers, operates alike on the philosopher

and on the savage.

To this belief in the permanent uniformity of

physical laws, Dr Reid long ago gave the name of

the inductive 'principle. ** It is from the force of

" this principle," he observed, *' that we immediately

" assent to that axiom upon which all our knowledge


" of nature is built, That effects of the same kind

" must have the same cause. For effects and causes,

** in the operations of nature, mean nothing but

*' signs, and the things signified by them. We per-

" ceive no proper causality or efficiency in any na-

" tural cause ; but only a connection established by

" the course of nature between it and what is called

*' its effects." *

A late celebrated writer, more distinguished by

the singular variety and versatility of his talents than

by the depth or soundness of his understanding,

was pleased to consider Reid's inductive principle

as a fit subject of ridicule ; asserting that the phe-

nomenon in question was easily explicable by the

common principles of ea^periencCy and the association

ofideas. *' Though no man," says he, " has had

" any experience of what is future, every man has

** had experience of what teas future." t Of the

shallowness of this solution philosophers are, I be-

lieve, now very generally convinced ; but even if the

case were otherwise, the Jact remarked by Reid

would be equally entitled to the attention of logi-

cians as the basis of all physical science, nor would

it be easy to distinguish it by a name less liable to

objection than that which he has selected.

In all Bacon's logical rules, the authority of this

* Inquiry into the Human Mind, Chap. vi. sect. 24.

t Priestley's Examination oi' lleid, Beattie, and Oswald, p. 85.

Some very judicious and decisive strictures on this theory of

Priestley may be found in Dr Campbell's Philosophy of Rheto-

ric. See note at the end of ihc sixth Chapter of Book i.

Sect. 1. OP THE HUMAN MIND. 3^1

law of belief is virtually recognised, although it is

nowhere formally stated in his writings ; and al-

though the doctrines connected with it do not seem

to be easily reconcileable with some of his occasional

expressions. It is, indeed, only of late that natural

philosophers have been fully aware of its importance

as the ground-work of the inductive logic j the ear-

lier writers under whose review it fell having been

led to consider it chiefly by its supposed subservien-

cy to their metaphysical or to their theological spe-

culations. Dr Reid and M. Turgot were, so far as

I know, the first who recognised its existence as an

original and ultimate law of the understanding ;

—

the source of all that experimental knowledge which

we begin to acquire from the moment of our birth,

as well as of those more recondite discoveries which

are dignified by the name of science. It is but

justice to Mr Hume to acknowledge, that his Trea-

tise of Human Nature furnished to Dr Reid all the

premises from which his conclusions were drawn5

and that he is, therefore, fairly entitled to the ho-

nour of having reduced logicians to the alternative

of either acquiescing in his sceptical inferences, or

of acknowledging the authority of some instinctive

principles of belief, overlooked in Locke's Analy-

sis.*

II. There is another circumstance which fre-

quently adds to the difficulty of tracing the laws of

nature ; and which imposes on the philosopher, while

carrying on the process of induction, the necessity

» Note (O.)

35^ ELEMENTS OF THE PHILOSOPHY Chap. IV.

of following a still more refined logic than has

been hitherto described.—When a uniformity is

observed in a number of different events, the curio-

sity is roused by the coincidence, and is sometimes

led insensibly to a general conclusion. In a few

other cases, a multiplicity of events, which appear to

common observers to be altogether anomalous, are

found, upon a more accurate and continued exami-

nation of them, to be subjected to a regular law. *

The cycles by which the ancients predicted eclipses

of the sun and moon ; the two laws inferred by Kep-

ler from the observations of Tycho Brahe ; the law

of refraction inferred by Snellius from the tables of

Kircher and Scheiner, are instances of very com-

prehensive and most important rules obtained by the

mere examination and comparison of particulars.

Such purely empirical discoveyies, however, are con-

fined almost entirely to optics and astronomy, in

which the physical laws combined together are com-

paratively few, and are insulated from the influence

of those incalculable accidents which, in general,

disturb the regularity of terrestrial phenomena. In

by far the greater number of instances, the appear-

ances of nature depend on a variety of different laws,

all of which are often combined together in produ-

cing one single event : And, wherever such a com-

bination happens, although each law may take place

with the most complete uniformity, it is likely that

nothing but confusion will strike the mere observer.

A collection of such results, therefore, would not

advance us one step in the knowledge of nature

;

* Philosophy of the Human Mind, Vol. I. Chap. vi. Sect. iv.

7

Stct. 1. OF THE HUMAN MIND. 353

nor would it enable us to anticipate the issue of one

new experiment. In cases of tliis description, be-

fore we can avail ourselves of our past experience,

we must employ our reasoning powers in comparing

a variety of instances together, in order to discover,

by a sort of analysis or decomposition, the simple

laws which are concerned in the phenomenon under

consideration ;—after which, wê may proceed safely,

in determining a ijriori what the result will be of

any hypothetical combination of them, whether total

or partial. *

These observations have led us to the same con-

clusion with that which forms the great outline of

Bacon's plan of philosophising ; and which Newton

has so successfully exemplified in his inquiries con-

cerning gravitation and the properties of light. While

they point out, too, the respective provinces and

* " Itaque naturae facieuda est prorsus solutio et separatio ;

' non per ignera certe, sed per mentem, tanquam igneni divi-

'' num." {Nov. Organ. Lib. II. Aphor. xvi.) The remainder of

the aphorism is equally worthy of attention ; in reading which,

however, as well as the rest of Bacon's philosophical works, I

must request, for a reason afterwards to be !mentioned, that the

word Law may be substituied iox Form, wherever it may occur.

—

An attention to this circumstance will be found of much use in

studying the Novum Organon.

A similar idea, under other metaphorical disguises, often occurs

in Bacon. Considering the circumstances in which he wrote, lo-

gical precision was altogether impossible; yet it is astonishing

Avith what force he conveys the spirit of the soundest philosophy

of the eighteenth century. " Neque enim in piano via sita est,

" sed ascendendo et descendendo ; ascendendo primo ad axiomata^

" descendendo ad opera."

—

Nov. Org. Lib. I, Aphor. cili.

VOL. II. Z

;^-'-

3d4 elements of the philosophy Chap. IV.

uses of the analytic and the synthetic methods, they

illustrate the etymological propriety of the names by

which, in the Newtonian School, they are contradis-

tinguished from each other.

In fact, the meaning of the words analysts and

synthesis, when applied to the two opposite modes of

investigation in physics, is extremely analogous to

their use in the practice of chemistry. The chief

difference lies in this, that, in the former case, they

refer to the logical processes of the understanding in

the study oiphysical laws ; in the latter, to the ope-

rative processes of the laboratory in the examination

of material substances.

If the foregoing remarks are well founded, they

lead to the correction of an oversight which occurs

in the ingenious and elegant sketch of the History

of Astronomy, lately puljlished among the posthu-

mous works of Mr Smith ; and which seems calcu-

lated to keep out of view, if not entirely to explode,

that essential distinction which I have been endea-

vouring to establish, between the inductive logic of

Bacon's followers, and the hypothetical theories of

their predecessors.

*' Philosophy," says Mr Smith, " is the science

" of the connecting principles of nature. Nature,

*' after the largest experience that common observa-

" tion can acquire, seems to abound with events

'* which appear solitary and incoherent with all that

" go before them ; which, therefore, disturb the

** easy movement of the imagination ; which make" its ideas succeed each other, if one may say so, by

" irregular starts and sallies j and which thus tend,

11


" in some measure, to introduce a confusion and dis-

" traction and giddiness of mind. Philosophy, by" representing the invisible chains which bind toge-

** ther all these disjointed objects, endeavours to in-

" troduce order into this chaos of jarring and dis-

" cordant appearances ; to allay this tumult of the

** imagination ; and to restore it, when it surveys

" the great revolutions of the universe, to that tone

" of tranquillity and composure, which is both most

" agreeable in itself, and most suitable to its nature.

" Philosophy, therefore, may be regarded as one of

" those arts which address themselves to the imagi-

*' nation, by rendering the theatre of nature a more" coherent, and, therefore, a more magnificent spec-

" tacle, than otherwise it would have appeared to be."

That this is one of the objects of philosophy, and

07ie of the advantages resulting from it, I very readi-

ly admit.—But, surely, it is not the leading object

of that plan of inductive investigation which was re-

commended by Bacon, and which has been so skil-

fully pursued by Newton. Of all philosophical sys-

tems, indeed, hypothetical or legitimate, it must be

allowed, tliat, to a certain degree, they both please

the imagination and assist the memory, by introdu-

cing order and arrangement among facts, which had

the appearance, before, of being altogether uncon-

nected and isolated. But it is the peculiar and ex-

clusive prerogative of a system fairly obtained by the

method of induction, that, while it enables us to ar-

range facts already known, it furnishes the means of

ascertaining, by synthetic reasoning, those which we

have no access to examine by direct observation.


The difference, besides, among hypothetical theories,

is merely a difference of degree, arising from the

greater or less ingenuity of their authors ; whereas

legitimate theories are distinguished from all others,

radicalli) and essenlially ; and, accordingly, while

the former are liable to perpetual vicissitudes, the

latter are as permanent as the laws which regulate

the order of the universe.

Mr Smith himself has been led, by this view of the

object of philosophy, into expressions concerning the

Newtonian discoveries, which seem to intimate, that,

although he thought them far superior, in point of

ingenuity, to anything the world had seen before,

yet, that he did not consider them as so completely

exclusive of a still happier system in time to come,

as the Newtonians are apt to imagine. ** The sys-

** tern of Newton," he observes, *' now prevails over

" all opposition, and has advanced to the acquisition

" of the most universal empire that was ever esta-

*' blished in philosophy. His principles, it must be

" acknowledged, have a degree of firmness and soli-

" dity that we should in vain look for in any other

" system. The most sceptical cannot avoid feeling

" this. They not only connect together most per-

*' fectly all the phenomena of the heavens which had

" been observed before his time ; but those also

** which the persevering industry and more perfect

" instruments of later astronomers have made known" to us, have been either easily and immediately ex-

" plained by the application of his principles, or have

*' been explained in consequence of more laborious

" and accurate calculations from these principles, than

10

Spct. 1. OF THE HUMAN MIND. 357

" had been instituted before. And even tre, while

" we have been endeavouring to represent all philoso-

** phical systems as mere inventions of the imagina-

" tion, to connect together the otherwise disjointed

" and discordant phenomena of nature, have insen-

" sibly been drawn in to make use of language ex-

" pressing the connecting principles of this one, as

" if they were the real chains which nature makes

" use of, to bind together her several operations."

If the view which I have given of Lord Bacon's

plan of investigation be just, it will follow, That the

Newtonian theory of gravitation can, in no respect

whatever, admit of a comparison with those systems

which are, in the slightest degree, the offspring of

imagination ; inasmuch as the principle employed to

explain the phenomena is not a hypothesis, but a ge-

neralfact established by induction ; for which fact

we have the very same evidence as for the various

particulars comprehended under it. The Newto-

nian theory of gravitation, therefore, and every other

theory which rests on a similar basis, is as little liable

to be supplanted by the labours of future ages, as the

mathematical conclusions of Euclid and Archimedes.

The doctrines which it involves may be delivered in

different, and perhaps less exceptionable forms ; but

till the order of the universe shall be regulated by

new physical laws, their substance must for ever re-

main essentially the same. On the chains, indeed,

"which nature makes use of to bind together her seve-

ral operations, Newton has thrown no light what-

ever ; nor was it the aim of his researches to do so.

The subjects of his reasonings were not occult con-


nections, but particular phenomena, and general

laws ;—^botli of them possessing all the evidence

which can belong toJewts ascertained by observation

and experiment. From the one or the other of

these all his inferences, whether analytical or syn-

thetical, are deduced : Nor is a single hypothesis in-

volved in his datcij excepting the authority of that

Law of Belief which is tacitly and necessarily as-

sumed in all our physical conclusions,—The stability

of the order of nature.

Section II.

Continuation ofthe Subject.—The InductiofiqfAriS'

totle compared tvith that ofBacon,

In this section I intend to offer a few slight re-

marks upon an assertion which has been hazarded

with some confidence in various late publications,

that the method of investigation, so much extolled by

the admirers of Lord Bacon, was not unknown to

Aristotle.—It is thus veiy strongly stated by the

ingenious author of a memoir in the Asiatic Re-

searches. *

" From some of the extracts contained in this

" paper, it will appear, 1st, That the mode of rea-

" soning by induction^ illustrated and improved by

" the great Lord Verulam in his Organum Novum," and generally considered as the cause of the rapid

" progress of science in later times, was perfectly

" /mown to Aristotle, and was distinctly delineated

* Asiatic Researches, Vol. VIII. p. 89, 90. London Edition.


" by him, as a method of investigation that leads to

" certainty or truth : and 2dly, That Aristotle was

" likewise perfectlj/ acquainted, not merely with the

" form of induction, but with the proper materials

*' to be employed in carrying it on—facts and expe-

" riments. We are therefore led to conclude, that

" all the blame of confining the human mind for so

" long a time in chains, by the force of syllogism,

" cannot be fairly imputed to Aristotle ; nor all the

" merit of enlarging it, and setting it free, ascribed

" to Lord Verulam."

The memoir from which this passage is copied,

consists of extracts translated (through the medium

of the Persian) from an Arabic treatise entitled the

Essence ofLogic. When it was first presented to

the Asiatic Society, the author informs us, that he

was altogether ignorant of the coincidence of his own

conclusions with those of Dr Gillies ; and he seems

to have received much satisfaction from the subse-

quent perusal of the proofs alleged in support of

their common opinion by that learned writer. " From" the perusal of this wonderful booky** Dr Gillies*s

exposition of the Ethics and Politics of Aristotle,

" I have now the satisfaction to discover, that the

" conjectures I had been led to draw from these

** scanty materials, are completely confirmed by the

" opinion of an author, who is probably better qua-

" lified than any preceding commentator on Aris-

" totle's works to decide on this subject." *

It is observed by Bailly, in his History of Astro=

* Ibid.

360 ELEMENTS OF THE PHILOSOPHY Chap. l\\

nomy, that, although frequent mention is made of

attraction in the writings of the ancients, we must

not therefore " conclude that they had^ any precise

" or just idea of that law into which Newton hasre-

" solved the phenomena of the planetary revolutions.

" To their conceptions, this word presented the no-

" tion of an occult sympathy between different ob-

" jects ; and if any of them extended it from the

*' descent of terrestrial bodies to explain the manner" in which the moon was retained in her orbit, it

" was only an exhibition upon a larger scale of the

" popular error." * The same author has remark-

ed, on a different occasion, that, in order to judge

of the philosophical ideas entertained at a particular

period, it would be necessary to possess the dictionary

of the age,—exhibiting the various shades of mean-

ing derived from fashion or from tradition. " The*' import of words," he adds, '* changes with the

*' times : their signification enlarging with the pro-

" gress of knowledge. Languages are every mo-" ment perishing in detail from the variations intro-

" duced by custom : they grow old like those that

" speak them, and, like them, gradually alter their

" features and their form." t

If this observation be just, with respect to the at-

traction of the ancients, when compared with the at-

traction of Newton, it will be found to apply with

still greater force to the induction of Aristotle, t

considered in contrast with the induction of Bacon.

* Hist, dc I'Astronomie Modeinc, Tome II. p. 555, 556.

+ Ibid. p. 184.

:j;ETaywyjj. Translated Inductio by Cicero.


It is well known to those who are at all conver-

sant with Bacon's writings, that, although he bor-

rowed many expressions from the scholastic phraseo-

logy then in vogue, he has, in general, not only

employed them in new acceptations, consonant to

the general spirit of his own logic, but has, by defi-

nitions or explanations, endeavoured to guard his

readers against the mistakes to which they might

be exposed, from a want of attention to the imiova-

tions thus introduced in the use of consecrated terms.

How far he judged wisely in adopting this plan

(which has certainly much injured his style in point

of perspicuity), I do not presume to decide ; I wish

only to state the fact :—his motives may be judged

of from his own words.

^' Nobis vero ex altera parte (quibus, quantum ca-

*' lamo valemus, inter vetera et nova in Uteris foedus

" et commercium contrahere, cordi est) decretum

" manet, antiquitatem comitari usque ad aras ; at-

" que vocabula antiqua retinere, quanquam sensum*' eorum et definitiones scepius iramutemus ; secun-

" dum moderatum ilium et laudatum, in Civilibus,

" novandi modum, quo rerum statu novato, verbo-

*' rum tamen solennia durent;quod notat Tacitus

;

" eadem mamstratuum vocabidaJ^ *'t>'

* De Aug. Scient. Lib. iii. cap. iv.

The necessity under which the anti-Aristotelians found them-

selves, in the earlier part of the seventeenth century, of disguis-

ing their attack on the prevailing tenets, is strongly illustrated

in a letter from Descartes to Regius. " Pourquoi rejettez-

" vous publiquement les qualites rcelles et les formes suhstan-

" tielles, si cheres aux scholastiques : J'ai declare, que je uq

S6Q ELEMENTS OF THE PHILOSOPHY Chap. IV^

Of these double significations, so common in Ba-

con's phraseology, a remarkable instance occurs in

the use which he makes of the scholastic word forms.

In one passage, he approves of the opinion of Plato,

that the investigation oi forms is the proper object

of science ; adding, however, that this is not true

of Xheforms which Plato had in view, but of a dif-

ferent sort 0^forms, more suited to the grasp of our

faculties. * In another passage, he observes, that

when he employs the word^rw5, in speaking of na-

tural philosophy, he is always to be understood as

meaning the laws of nature, t Whether so accu-

rate a reasoner as Locke would have admitted Ba-

con's general apology for so glaring an abuse of

xcords, may perhaps be doubted : but, after com-

paring the two foregoing sentences, would Locke

" pretendois pas les nier, mais que je n'en avois pas besoin

" pour expliquer mes pensees."

* " Manifestum est, Platonem, virum sublimis ingenii (qui-

" que veluti ex rupe excelsa omnia circumspiciebat) in sua de

*' ideis AoctYma.,formas esse verum scientice objectmn, vidisse

;

" utcunque sentential hujus verissimas fructum amisent,Jbnnag" penitus a materia abstractas, non in materia determinatas

" contemplando et prensando. Quod si diligenter, serio, et

" sincere, ad actionem, et usum, et oculos convertamus ; non" difficile crit disquirere, et notitiam assequi, quae sint iWsefor-

" mce, quarum cognitio res humanas meris modis locupletare et

" beare possit."

—

De Augment. Sclent. Lib. iii. cap. iv.

-|- " Nos quum de formis loquimur, nil aliud intelligimus,

" quam leges illas, quae naturam aliquam simplicem ordinant

" et constituunt ; ut calorem, lumen, pondus, in omnimoda ma-

*' teria et subjecto susceptibili. Itaque eadem res est forma" calidi, autforma luminis, et kx calidi, sive lex luminis,"

—

Nov. Org. Lib. ii. Aph. xvii.

Sect. 2. OF THE HUMAN MIND* S^S

(notwithstanding his ign.orance of the syllogistic art)

have inferred, that Bacon's opinion of the proper

object of science was the same with that of Plato ?

The attempt to identify Bacon's induction with the

induction of Aristotle, is (as I trust will immediate-

ly appear) infinitely more extravagant. It is like

confounding the Christian Graces with the Graces

of Heathen Mythology.

The passages in which Bacon has been at pains

to guard against the possibility of such a mistake

are so numerous, that it is surprising how any per-

son, who had ever turned over the pages of the No-

vum Organon, should have been so unlucky as not

to have lighted upon some one of them. The two

following will suffice for my present purpose :

" In constituendo autem axiomate, forma induc-

** tionis alia quam adhuc in usu fuit, excogitanda

*' est. Inductio enim quee procedit per eniimera-

" tionem simplicem res puerilis est, et precario con-

" cludit. At inductio^ quae ad inventionem et de-

" monstrationem scientiarum et artium erit utilis,

" naturam separare debet, per rejectiones et exclu-

" siones debitas ; ac deinde post negativas tot quot

" sufficiunt, super affirmativas concluderejquod ad-

" hue factum non est, nee tentatum certe, nisi tan-

" tummodo a Platone, qui ad excutiendas defini-

*' tiones et idseas, hac certe forma inductionis aliqua-

" tenus utitur. Verum ad hujus inductionis, sive

" demonstrationis instructionem bonam et legiti-

" mam, quamplurima adhibenda sunt, quae adhuc

** nulHus mortalium cogitationem subiere ; adeo ut

" in ea major sit consumenda opera, quam adhuc

364. ELEMENTS OF THE PHILOSOPHY Chap. IV.

" consumpta est in syllogismo. Atqiie i?i hac certc

" inductiotiey spes maxima sita est." *

*' Cogitavit et illucl— Restare indiictionem,

" tanquam ultimum et unicmii rebus subsidium et

** perfugimn, Verum et hujus nomen tantmnmodo

*' notmn esse ; vim et iisiim homines hactenus la-

" tuisse.'* t

That I may not, however, be accused of resting

my judgment entirely upon evidence derived from

Bacon's writings, it may be proper to consider more

particularly to what the induction of Aristotle really

amounted, and in what respects it coincided with

that to which Bacon has extended the same name.

*' Our belief,'* says Aristotle in one passage, " is,

" in every instance, founded either on syllogism or in-

'" duction." To which observation he adds, in the

course of the same chapter, that *' induction is an

** inference drawn from all the particulars which it

" comprehends." X It is manifest, that, upon this

occasion, Aristotle speaks of that induction which

Bacon, in one of the extracts quoted above, describes

* Nov. Org. Lib. i. Aph. cv.

\ Cogltata et Visa. The short tract to which Bacon has pre-

fixed this title, contains a summar}^ of what he seems to have

considered as the leading tenets of his philosophical works. It

is one of the most highly finished of all his pieces, and is

marked throughout with an impressive brevity and solemnity,

which commands and concentrates the attention. Nor does it

affect to disguise that consciousness of intellectual force, which

might be expected from a man destined to fix a new sera in the

history of human reason.

—

Franciscus Baconus sic cogita-

vit, &c, &-C.

% First Analytics, Chap, xxiii. Vol. I. p. 126. Edit.Du Val.


as proceeding by simple enumeration ; and which he,

therefore, pronomices to be " a puerile employment** of the mind, and a mode of reasoning leading to

** uncertain conclusions." In confirmation of Ba-

con's remark, it is sufficient to mention, by way of

illustration, a single example ; which example, to

prevent cavils, I shall borrow from one of the high-

est loo'ical authorities,—Dr Wallis of Oxford.

*' In an inference from induction,*' says this learn-

ed writer, "if the enumeration be complete, the evi-

" dence will be equal to that of a perfect syllogism;

"as if a person should argue, that all the planets

*' (the Sun excepted) borrow their light from the

" Sun, by proving this separately of Saturn, Jupiter,

*' Mars, Venus, Mercury, and the Moon. It is,

" in fact, a syllogism in Daraptiy of which this is

** the form

:

" Saturn^ Jupiter, MarSy Veniis^ Mercury, and" the Moon, each borrow their lightfrom the

" Sun

:

" But this enumeration comprehends all the Pla-

*' nets, the Sun excepted :

*' Therefore all the Planets (the Sun crcept-

" edj borrow their lightfôm the Sun.'* *

* Institutio Logica, Lib. iii. cap. 15. The reasoning em-

ployed by Wallis to shew that the above is a legitimate syllo-

gism in Darapti, affords a specimen of the facility with which

a logical conjuror can transform the same argument into the

most different shapes. " Siquis objiciat, hunc non esse legiti-

" mum in Darapti syllogismum, eo quod conclusionem habeat

" universalem ; dicendum erit, hanc universalem (qualis qualis

" est) esse universalem collectivam ; quse singularis est, Est-


If the object of Wallis had been to expose the

jpiienliti/ and the precarkmsness of such an argu-

ment, he could not possibly have selected a happier

illustration. The induction of Aristotle, when con-

sidered in tilts light, is indeed a fit companion for

his syllogism ; inasmuch, as neither can possibly ad-

vance us a single step in the acquisition of new know-

ledge. Kow different from both is the induction of

Bacon, which, instead of carrying the mind round

in the same circle of words, leads it from the past to

theJiiture, from the knoxvn to the iinkno'wn ?*

*' que vox omnis hie loci (quae dici solet) pars Categorematica ;

" utpote pars termini minoris (ut ex minori propositione liquet)

" qui hie est (non Plaueta; seel) omnes Planetcc (excepto sole),

** seu tota collectio reliquorum (excepto sole) Planetarum,

" quae collectio unica est ; adeoque conclusio singidaris. Quae*' quidem (ut singulares aliae), quamvis sit propositio Universa-

" lis, vi materiae ; non tamen talis est ut non possit esse con-

*' clusio in tertia figura. Quippe in tertia figura, quoties minor

" terminus, seu praedicatum minoris propositionis (adeoque sub-

" jectum conclusionis) est quid singulare, necesse estut conclu-

** sio ea sit (vi materiae, non formse) ejusmodi univeralis,"

In justice to Dr Wallis, it is proper to subjoin to these quo-

tations a short extract from the dedication prefixed to this trea-

tise.—" Exempla retineo, quae apud logicos trita sunt ; ex phi-

*' losophia quam vocant Veterem et Peripateticam petita : quia

" logicam hie trado, et quidem Peripateticam ; non naturalem

" philosophiam. Adeoque, de quatuor elemcntis ; de telluris

*' quiete in universi medio ; de gravium motu deorsum, levium-

" que sursum ; de septenario planetarum numero, aliisque ; sic

" loquor, ut loqui solent Peripatetici."

* " In arte judicandi (ut etiam vulgo receptum est) aut per

*' Inductionem, aut per Syllogismum coneluditur. At quate-

" nus ad judicium, quod fit per inductionem, nihil est, quod

'• nos detinere debeat : uno siquiclem eodemque mentis opere it'

Sect. 2. OF THE HUMAN BUND. 367

Dr Wallis afterwards very justly remarks, " that

" inductions of this sort are of frequent use in ma-

" thematical demonstrations ; in which, after enu-

" merating all the possible cases, it is proved, that

" the proposition in question is true of each of these

** considered separately ; and the general conclusion

*' is thence drawn, that the theorem holds universal-

" ly. Thus, if it were shewn, that, in all right-

" angled triangles, the three angles are equal to two

" right angles, and that the same thing is true in all

*' acute-angled, and also in all obtuse-angled tri-

" angles ; it would necessarily follow, that in every

*' triangle the three angles are equal to two right

" angles ; these three cases manifestly exhausting all

" the possible varieties of which the hypothesis is

** susceptible."

My chief motive for introducing this last passage

was to correct an idea, which, it is not impossible,

may have contributed to mislead some of Wallis's

readers. As the professed design of the treatise in

question was to expound the logic of Aristotle, a-

greeably to the views of its original author ; and as

all its examples and illustrations assume as truths the

Peripatetic tenets, it was not unnatural to refer to

the same venerated source the few incidental reflec-

tions with which Wallis has enriched his work. Of

this number is the foregoing remark, which differs

so very widely from Aristotle's account of mathema-

" lud quod quceritur, et invenitur etjudkatur.—At inductionis

" formam vitiosam prorsus/valere jubemus ; legitimam ad No-'' vum Organum reraittimus."—-Z>e Aug, Scient. Lib. v. cap, iv.


tical induction, that I was anxious to bring the two

opinions into immediate contrast. The following is

a faithful translation from Aristotle's own words :

" If any person were to shew, by particular de-

" monstrations, that every triangle, separately con-

" sidered, the equilateral, the scalene, and the isos-

** celes, has its three angles equal to two right angles,

** he would not, therefore^ know that the three

** angles of a triangle are equal to two right angles,

** except after a sophistical manner. Nor would he

** know this as an universal property of a triangle,

" although, beside these, no other triangle can be

" conceived to exist ; for he does not know that it

* belongs to it qua triangle : Nor that it belongs

*' to every triangle, excepting in regard to number ;

*' his knowledge not extending to it as a property

' of the genus, although it is impossible that there

*' should be an individual which that genus does not

" include." *

* A/a rsro ouS' av ric, dei'^ri %aS haffrov to rîyomv a'::ooeit,e(

% fjjic(, 71 srsâ, on dvo o^Sai lyei exaffrov, to ido'TrAiuôv %w^'e, >y to

Gxoiknwv, }y to iGoazsKig' oicTw oih to Tgiyuvov or/ dvo o^dcug i<Sov, «

[ir^ Tov go^kSti-aov tôttov ovos xa&o'Ais Toiyuvov, o-jb' et fitihiv iCri rraêt

TOLUTa Tîyuvov sTiPov ou ya^, jj Tîyuvov oidsv ouSi itav Tîyuvov, aXX

r xar aîdfiov %a.T eihoc, hi ou rrav, >y et fxr^div iCrtv 6 ovx oios.—Analyt. Poster. Lib. i. cap. v.

1 have rendered the last clause according to the best of my

judgment ; but, in case of any misapprehension on my part, I

have transcribed the author's words. It may be proper to men-

tion, that this illustration is not produced by Aristotle as an in-

stance of induction ; but it obviously falls under his own defini-

tion of it, and is accordingly considered in that light by Dr

Wallis.


For what reason Aristotle should have thought of

applying to such an induction as this the epithet

sophistical, it is difficult to conjecture. That it is

more tedious, and therefore less elegant, than a ge-

neral demonstration of the same theorem, is un-

doubtedly true ; but it is not on that account the

less logical, nor, in point of form, the less rigorously

geometrical. It is, indeed, precisely on the same

footing with the proof of every mathematical pro-

position which has not yet been pushed to the ut-

most possible limit of generalization.

It is somewhat curious, that this hypothetical ex-

ample of Aristotle is recorded as a historical fact by

Proclus, in his commentary on Euclid. *' One" person, we are told,'* (I quote the words of MrMaclaurin,) ** discovered, that the three angles of

** an equilateral triangle are equal to two right angles;

" another went farther, and shewed the same thing

" of those that have two sides equal, and are called

** isosceles triangles : and it was a third that found*' that the theorem was general, and extended to

" triangles of all sorts. In like manner, when the

" science was farther advanced, and they came to

** treat of the conic sections, the plane of the sec-

" tion was always supposed perpendicular to the side

*' of the cone ; the parabola was the only section

*' that was considered in the right-angled cone, the

" ellipse in the acute-angled cone, and the hyper-

" bola in the obtuse-angled. From these three

** sorts of cones, the figures of the sections had their

" names for a considerable time j till, at length, A=

VOL. II. A a

370 ELEMENTS OF THE PHILOSOPHY Chap. I\',

" pollonius shewed that they might all be cut out of

" any one cone, and, by this discovery, merited in

" those days the appellation of the Great Geometri-

" cian." *

It would appear, therefore, that, in mathematics,

an inductive inference may not only be demonstra-

tively certain, but that it is a natural, and sometimes

perhaps a necessary step, in the generalization of our

knowledge. And yet it is of one of the most unex-

ceptionable inductive conclusions in this science

(the only science in which it is easy to conceive an

enumeration which excludes the possibility of any

addition) that Aristotle has spoken,—as a conclu-

sion resting on sophistical evidence.

So much with respect to Aristotle's induction^ on

the supposition that the enumeration is complete.

In cases where the enumeration is imperfect, DrWallis afterwards observes, *' That our conclusion

" can only amount to a probability or to a conjec-

" ture ; and is always liable to be overturned by aii

" instance to the contrary." He observe's also,

" That this sort of reasoning is the principal instru-

" ment of investigation in what is now called eaye-

" rimental philosophy ; in which, by observing and

" examining particulars, we arrive at the knowledge

" of universal truths." t All this is clearly and

correctly expressed j but it must not be forgotten,

* Account of Sir Isaac Newton's Phil. Discoveries, Book. i.

Chap. V.

f Institutio Logica.—See the Chapter De Inductione et Ex-

emplo.

7

•Sect. •:. <>^ THE HUMAN MIND. 371

tiiat it is the language of a writer trained in the

schools of Bacon and of Newton.

Even, however, the induction here described by

Dr Wallis falls greatly short of the method of phi-

losophising pointed out in the Novum Organon. It

coincides exactly with those empirical inferences

from mere experience, of which Bacon entertained

such slender hopes for the advancement of science.

*' Kestat experientia mera;qu£e si occurrat, casus ;

" si quaesita sit, experimentum nominatur. Hoc" autem experientias genus nihil aliud est, quam" mera palpatio, quali homines noctu utuntur, omnia

" pertentando, si forte in rectam viam incidere de-

*' tur ;quibus multo satius et consultius foret, diem

" praestolari aut lumen accendere, deinceps viam

" inire. At contra, verus experientiê ordo primo*' lumen accendit, deinde per lumen iter demon-'* strat, incipiendo ab experientia ordinata et di-^

" gesta, et minime prjrpostera aut erratica, atque ex

" ea educendo axiomata, atque ex axiomatibus con-

" stitutis rursus experimenta nova, quum nee ver-

** bum diviimm in rerum massam absque ordine ope-

** ratum sit."*

It is a common mistake, in the logical phraseo-

logy of the present times, to confound the words ex-

perience and induction as controvertible terms, t

Nov. Org. Aph. Ixxxii.

f " Let it always be remembered, that the author who first

*^ taught this doctrine {that the true art of reasoning is nothing

" but a language accurately defined and shilfully arranged),

*' had previously endeavoured to prove, that all our notions, as

•* well as the signs by which they are expressed, originate irt

372 ELEMENTS OF THE PHILOSOPHY Chap. IV»

There is, indeed, between them a very close affi-

nityJinasmuch as it is on experience alone that

every legitimate induction must be raised. The pro-

cess of induction, therefore, presupposes that of expe-

rience ; but, according to Bacon's views, the process

of experience does by no means imply any idea of

induction. Of this method. Bacon has repeatedly

said, that it proceeds " by means of rejections and

" exclusions" (that is, to adopt the phraseology of

the Newtonians, in the way oi anali/sisj to separate

or decompose nature ; so as to arrive at those axioms

or general laws, from which we may infer (in the

way of synthesis) other particulars formerly unknown

to us, and perhaps placed beyond the reach of our

direct examination. *

" perceptions of sense ; and that the principles on which lan-

" guages are first constructed, as well as every step in their pro-

" gress to perfection, all ultimately depend on inductions Jroni

" observation ; in one ivord, on experience merely."—Aris"

totle's Ethics and Politics by Gillies, Vol. I. pp. 94, 95.

In the latter of these pages, I observe the following sentence,

which isof itself sufficient to shew what notion the Aristotelians

still annex to the word under consideration. " Every kind of

" reasoning is carried on either by syllogism or by induction

;

" the former proving to us, that a particular proposition is true,

" because it isdeducible from a general one, already known to

** us ; and the latter demonstrating a general truth, because it

" holds in all particular cases."

It is obvious, that this species of induction never can be of the

slightest use in the study of nature, where the phenomena which

it is our aim to classify under their general laws are, in respect

of number, if not infinite, at least incalculable and incomprehen-

sible by our faculties.

* Nov. Org* Apb. cv. ciiL.

Sect 3. OF THE HUMAN MIND. S7S

But enough, and more than enougli, has been al-

ready said to enable my readers to judge how far

the assertion is correct, that the induction of Bacon

was well known to Aristotle. Whether it be yet

well knoxvn to all his commentators, is a different

question ; with the discussion of which I do not

think it necessary to interrupt any longer the pro-

gress of my work.

Section III.

Of the Import of the Words Analysis and Synthe-

sis, in the Language qf^Modern Philosophy,

As the words Analysis and Synthesis are now be-

come of constant and necessary use in all the differ-

ent departments of knowledge ; and as there is rea-

son to suspect, that they are often employed with-

out due attention to the various modifications of their

import, which must be the consequence of this va-

riety in their application,—it may be proper, before

proceeding farther, to illustrate, by a few examples,

their true logical meaning in those branches of sci-

ence, to which I have the most frequent occasions

to refer in the course of these inquiries. I begin

with some remarks on their primary signification in

that science, from which they have been transferred

by the moderns to Physics, to Chemistry, and t-?

the Philosophy of thQ Human Mind.

574 ELEMENTS OF THE PHILOSOPHY Chap. IV'

I.

Preliminary/ Observations on the Analysis and Syn^

thesis of the Greek Geometricians.

It appears from a very interesting relic of an an-

cient writer, * that, among the Greek geometri-

cians, two different sorts of analysis were employed

as aids or guides to the inventive powers ; the one

adapted to the solution of problems ; the other to

the demonstration of theorems. Of the former of

these, many beautiful exemplifications have been

long in the hands of mathematical students ; and of

the latter (which has drawn much less attention in

modern times), a satisfactory idea may be formed

from a series of propositions published at Edinburgh

about fifty years ago. t I do not, however, know

.

that any person has yet turned his thoughts to an

examination of the deep and subtle logic displayed

in these analytical investigations ; although it is a

subject well worth the study of those who delight in

tracing the steps by which the mind proceeds in pur-

suit of scientific discoveries. This desideratum it is

not my present purpose to make any attempt to sup-

ply ; but only to convey such general notions as

may prevent my readers from falling into the com-

* Preface to the seventh book oC the Mathematical Collec»

tions of Pappus Alexandrinus. An extract from the Latin ver-

sion of it by Dr Halley may be found in Note (P.)

f Propositiones Geometricae More Veterum Demonstratae.

Auctore Matthaeo Stewart, S. T. P. Matheseos in Academia

Edinensi Professore, 1763.


moil error of confounding tlie analysis and synthesis

of tlie Greek Geometiy, with tlie analysis and syn-

thesis of the Inductive Philosophy.

In the arrangement of the following hints, I shall

consider, in the first place, the nature and use of

analysis in investigating the demonstration of the-

orems.—For such an application of it, various oc-

casions must be constantly presenting themselves to

every geometer ;—when engaged, for example, in

the search of more elegant modes of demonstrating

propositions previously brought to light ; or in as-

certaining the truth of dubious theorems, which,

from analogy, or other accidental circumstances,

possess a degree of verisimilitude sufficient to

rouse the curiosity.

In order to make myself intelligible to those who

are acquainted only with that form of reasoning

which is used by Euclid, it is necessary to remind

them that the enunciation of every mathematical pro-

position consists of two parts. In the first place, cer-

tain suppositions are made ; and secondly, a certain

consequence is affirmed to follow from these suppo-

sitions. In all the demonstrations which are to be

found in Euclid's Elements (with the exception of

the small number of indirect demonstrations), the

particulars involved in the hypothetical part of the

enunciation are assumed as the principles of our

reasoning ; and from these principles, a series or

chain of consequences is, link by link, deduced, till

we at last arrive at the conclusion which the enun-

ciation of the proposition asserted as a truth, A


demonstration of this kind is called a Synthetical

demonstration.

Suppose now, that I arrange the steps of myreasoning in the reverse order ; that I assume hy-

pothetically the truth of the proposition which I

wish to demonstrate, and proceed to deduce from

this assumption, as a principle, the different conse-

quences to which it leads. If, in this deduction, I

arrive at a consequence which I already know to be

ti'ue, I conclude with confidence, that the principle

from which it was deduced is likewise true. But if,

on the other hand, I arrive at a consequence which

I know to be false, I conclude, that the principle or

assumption on which my reasoning has proceeded is

false also.—Such a demonstration of the truth or

falsity of a proposition is called an Analytical de-

monstration.

According to these definitions of Analysis and

Synthesis, those demonstrations in Euclid which

prove a proposition to be true, by shewing, that the

contrary supposition leads to some absurd inference,

are, properly speaking, analytical processes of rea-

soning.—In every case, the conclusiveness of an

analytical proof rests on this general maxim. That

truth is always consistent with itself; that a suppo-

sition which leads, by a concatenation of mathema-

tical deductions, to a consequence which is true,

must itself be true ; and that which necessarily in-

volves a consequence which is absurd or impossible,

must itself be false.

r It is evident, that, when we are demonstrating a

proposition with a view to convince another of its


truth, the synthetic form of reasoning is the more

natural and pleasing of the two ; as it leads the un-

derstanding directly from known truths to such as

are unknown. AAîen a proposition, however, is

doubtful, and we wish to satisfy our own minds

with respect to it ; or when we wish to discover a

new method of demonstrating a theorem previously

ascertained to be true ; it will be found (as I already

hinted) far more convenient to conduct the investi-

gation analytically. The justness of this remark is

universally acknowledged by all who have ever exer-

cised their ingenuity in mathematical inquiries ; and

must be obvious to every one who has the curiosity

to make the experiment. It is not, however, so

easy to point out the principle on which this re-

markable difference between these two opposite in-

tellectual processes depends. The suggestions which

I am now to offer appear to myself to touch upon

the most essential circumstance ; but I am perfectly

aware, that they by no means amount to a complete

solution of the difficulty.

Let it be supposed, then, either that a new de-

monstration is required of an old theorem ; or, that

a new and doubtful theorem is proposed as a subject

of examination. In what manner shall I set to work,

in order to discover the necessary media of proof ?

—

From the hypothetical part of the enunciation, it is

probable, that a great variety of different conse-

quences may be immediately deducible ; from each

of which consequences, a series of other conse-

quences will follow : At the same time, it is pos-

sible, that only one or two of these trains of rea-

378 ELEMENTS OF THE PHILOSOPHY Chap. IV,

soning may lead the way to the trutli which I wish

to demonstrate. By what rule am I to be guided

in selecting the line of deduction which I am here

to pursue? The only expedient which seems to

present itself, is merely tentative or experimental

;

to assume successively all the different proximate

consequences as the Jirst link of the chain, and to

follow out the deduction from each of them, till I,

at last, find myself conducted to the truth which I

am anxious to reach. According to this supposi-

tion, I merely grope my way in the dark, without

rule or method : the object I am in quest of may,

after all my labour, elude my search ; and even, if

I should be so fortunate as to attain it, my success

affords me no lights whatever to guicje me in future

on a similar occasion.

Suppose now that I reverse this order, and prose-

cute the investigation analytically ; assuming (agree-

ably to the explanation already given) the proposi-

tion to be true, and attempting, from this supposi-

tion, to deduce some acknowledged truth as a neces-

saiy consequence. I have here one fixed point from

which I am to set out ; or, in other words, one

specific principle or datum from which all my con-

sequences are to be deduced ; while it is perfectly

immaterial in what particular conclusion my deduc-

tion terminates, provided this conclusion be pre-

viously known to be true. Instead, therefore, of

being limited, as before, to one conclusion exclu-

sively^ and left in a state of uncertainty where to

begin the investigation, I have one single supposi-

tiau marked out to me, frjom which my departure

Sect, 3. OF THE HUMAN MIND. 379

must necessarily be taken ; while, at the same

time, the path which I follow may teiininate with

equal advantage in a variety of different conclusions.

In the former case, the procedure of the understand-

ing bears some analogy to that of a foreign spy,

landed in a remote corner of this island, and left to

explore, by his own sagacity, the road to London.

In tlie latter case, it may be compared to that of an

inhabitant of the metropolis, who wished to effect

an escape, by any one of our sea-ports, to the con-

tinent. It is scarcely necessary to add, that as this

fugitive,—^should he happen, after reaching the

coast, to alter his intentions,-—would easily retrace

the way to his own home ; so the geometer, when

he has once obtained a conclusion in manifest har-

mony with the known principles of his science, has

only to return upon his own steps (cceca regensjilo

vestigia)^ in order to convert his analysis into a di-

rect synthetical proof.

A palpable and familiar illustration (at least in

some of the most essential points) of the relation in

which the two methods now described stand to

each other, is presented to us by the operation of

unloosing a difficult knot, in order to ascertain the

exact process by which it was formed. The illus-

tration appears to me to be the more apposite, that

I have no doubt it was this very analogy which sug-

gested to the Greek geometers the metaphorical ex-

pressions of analysis and of solution, which they

have transmitted to the philosophical language of

modern times.

Suppose a knot, of a very artificial construQtionj

/


to be put into my hands as an exercise for my in-

genuity, and that I was required to investigate a

rule, which others, as well as myself, might be able

to follow in practice, for making knots of the same

sort. If I were to proceed in this attempt, accord-

ing to the spirit of a geometrical synthesis, I should

have to try, one after another, all the various experi-

ments which my fancy could devise, till I had, at

last, hit upon the particular knot I was anxious to

tie. Such a process, however, would evidently be

so completely tentative, and its final success would,

after all, be so extremely doubtful, that common

sense could not fail to suggest immediately the idea

of tracing tJie knot through all the various complica-

tions of its progress, by cautiously undoing or un-

knitting each successive turn of the thread in a re-

trograde order, from the last to theJirst. After

gaining this^r^^ step, were all the former complica-

tions restored again, by an inverse repetition of the

same operations which I had performed in undoing

them, an infallible rule would be obtained for solving

the problem originally proposed ; and, at the same

time, some address or dexterity, in the practice of

the general method^ probably gained, which would

encourage me to undertake, upon future occasions,

still more arduous tasks of a similar description.

The parallel between this obvious suggestion of rea-

son, and the refined logic of the Greek analysis, un-

doubtedly fails in several particulars ; but both pro-

ceed so much on the same cardinal principle, as to

account sufficiently for a transference of the same

expressions from the one to the other. That this


triinsference has actually taken place in the instance

now under consideration, the literal and primitive

impoii of the words avcc and Auc;<5, affords as strong

presumptive evidence as can well be expected in any

etymological speculation.

In applying the method of analysis to geometrical

problems, the investigation begins by supposing the

problem to be solved ; after which, a chain of conse-

quences is deduced from this supposition, termi-

nating at last in a conclusion, which either resolves

into another problem, previously known to be within

the reach of our resources ; or which involves an

operation known to be impracticable. In the former

case, all that remains to be done, is to refer to the

construction of the problem in which the analysis

terminates ; and then, by reversing our steps, to de-

monstrate synthetically, that this construction fulfils

all the conditions of the problem in question. If it

should appear, in the course of the composition, that

in certain cases the problem is possible, and in

others not, the specification of these different

cases (called by the Greek geometers the Siopufj.G'i

or determinatiofi) becomes an indispensable requi-

site towards a complete solution.

The utility of the ancient analysis in facilitating

the solution of problems, is still more manifest than

in facilitating the demonstration of theorems ; and,

in all probability, was perceived by mathematician vS

at an earlier period. The steps by which it pro-

ceeds in quest of the thing sought, are faithfully

copied (as might be easily shewn) from that natural

logic which a sagacious mind would employ in simi-

S82 ELEMENTS OP THE PHILOSOPHY Chap. IV.

lar circumstances ; and are, in fact, but a scientific

application of certain rules of method, collected from

the successful investigations of men who were guid-

ed merely by the light of common sense. The

same observation may be applied to the analytical

processes of the algebraical art.

In order to increase, as far as the state of mathe-

matical science then permitted, the powers of their

analysis, the ancients, as appears from Pappus, wrote

thirty-three different treatises (known among ma-

thematicians by the name of tottos cx.vcchvoiJ.evo^), of

which number there are twenty-four books, whereof

Pappus has particularly described the subjects and

the contents. In what manner some of these were

instrumental in accomplishing their purpose, has

been fully explained by different modern writers

;

particularly by the late very learned Dr Simson of

Glasgow. Of Euclid's Data (for example), the

first in order of those enumerated by Pappus, he ob-

serves, that " it is of the most general and necessa-

" ry use in the solution of problems of every kind

;

" and that whoever tries to investigate the solutions

" of problems geometrically, will soon find this to

** be true ; for the analysis of a problem requires,

" that consequences be drawn from the things that

" are give/ij until the thing that is sought be shewn

*' to be giveji also. Now, supposing that the Data** were not extant, these consequences must, in

'* every particular instance, be found out and de-

'* monstrated from the things given in the enuncia-

" tion of the problem ; whereas the possession of

" this elementary book supersedes the necessity of


" anything more than a reference to the proposi-

" tions which it contains.'* *

With respect to some of the other books men-

tioned by Pappus, it is remarked by Dr Simson's

biographer, that *' they relate to general problems

" of frequent recurrence in geometrical investiga-

*' tions : and that their use was for the more imme-** diate resolution of any proposed geometrical pro-

** blem, which could be easily reduced to a particu-

** lar case of any one ofthem. By such a reduction,

" the problem was considered as fully resolved ; be-

" cause it was then necessary only to apply the ana-

" lysis, composition, and determination of that case

** of the general problem, to this particular problem

" which it was shewn to comprehend.'* t

From these quotations it manifestly appears, that

the greater part of what was formerly said of the

utility of analysis in investigating the demonstration

of theorems, is applicable, mutatis mutandis, to its

employment in the solution of problems. It appears

farther, that one great aim of the subsidiary books,

comprehended under the title of tottos avaAvofxevcs,

was to multiply the number of such conclusions as

might secure to the geometer a legitimate syntheti-

cal demonstration, by returning backwards, step by

step, from a known or elementary construction. Theobvious effect of this wâs, at once to abridge the

* Letter from Dr Simson to George Lewis Scott, Esq. pub-

lished by Dr Traill. See his Account of Dr Simson's Life and

Writings, p. 118.

i Ibid. pp. 159, 1^0.

S84f ELEMENTS OF THE PHILOSOPHY Chap. IV".

analytical process, and to enlarge its resources ;—ôn

a principle somewhat analogous to the increased fa-

cilities which a fugitive from Great Britain would

o-ain, in consequence of the multiplication of our

sea-ports.

Notwithstanding, however, the immense aids af-

forded to the geometer by the ancient analysis, it

must not be imagined that it altogether supersedes

the necessity of ingenuity and invention. It dimi-

nishes, indeed, to a wonderful degree, the number

of his tentative experiments, and of the paths by

which he might go astray ;* but (not to mention

the prospective address which it supposes, in pre-

paring the way for the subsequent investigation, by

a suitable constructio?i of the diagram) it leaves

much to be supplied, at every step, by sagacity and

practical skill ; nor does the knowledge of it, till

disciplined and perfected by long habit, fall under

the description of that S'vvccfjiLi a.vcbhvrix.Ti, which is

justly represented by an old Greek writer, t as an

acquisition of greater value than the most extensive

acquaintance with particular mathematical truths.

According to the opinion of a modern geometer

* " Nihil a ver^ etgenuin^ analysi magis distat, nihil magis

" abhorret, qudm tentandi method us ; hanc enim amovere et cer-

*' tissimd via ad qujesitum perducerc, prsecipuus est analyscos

" finis."

Extract from a MS. of Dr Simson, published by Dr Traill.

See his Account, &c. p. 127.

+ See the preface of Marinus to Euclid's Data. In the pre-

face to the 7th book of Pappus, the same idea is expressed by

the phrase bwaiiic, ivîruy}.

11

Sect. 3. OF THE HUMAN MIND. oS5

and philosopher of the first eminence, the genius

thus displayed in conducting the aj^proachcs to <i

preconceived mathematical conclusion, is of a far

liigher order than that which is evinced by the dis-

covery of new theorems. " Longe sublimioris in-

** genii est," says Galileo, " alieni Problematis eno-

" datio, aut ostensio Theorematis, quam novi cujus-

^* piam inventio : hjEC quippe fortuna? in incertuni

" vagantibus obvia^ plerumque esse solent ; tota vero

" ilia, quanta est, studiosissimam attenta3 mentis, in

** unum aliquem scopum collimantis, rationem ex-

*' poscit." * Of the justness of this observation, on

the whole, I have no doubt ; and have only to add

to it, by way of comment, that it is chiefly while

engaged in the steady pursuit of a particular object,

that those discoveries which are commonly consider-

ed as entirely accidental, are most likely to present

themselves to the' geometer. It is the methodical

inquirer alone who is entitled to, expect such fortu-

nate occurrences as Galileo speaks of ; and wher-

ever invention appears as a characteristical quality

of the mind, we may be assured, that something

more than chance has contributed to its success.

On this occasion, the fine and deep reflection of

Pontenelle will be found to apply with peculiar

* Not having the works of Galileo at hanil, I quote this pn«-

sage on the authority of Guide Grandi, who has introduced it in

the preface to his d( mons^tration of IIuyghcn'>'s Theorems con-

cerning the Logarithmic Line.—Vid, Hugenii Oprra Reliqua.

Tom. L p. 43.

VOL. II. B b


force : " Ces hasards ne sont que pour ceux qui

"joue7it bie?!.'^

II.

Critical Remarks on the vague Use, among Mo-dern WriterSy of the Terms Analysis and Syn-

thesis.

The foregoing observations on the Analysis and

Si/tithesis of the Greek Geometers may, at first

sight, appear somewhat out of place, in a disquisi-

tion concerning the principles and rules of the In-

ductive Logic. As it was, however, from the Ma-

thematical Sciences that these words were con-

fessedly borrowed by the experimental inquirers of

the Newtonian school, an attempt to illustrate their

original technical import seemed to form a necessary

introduction to the strictures which I am about to

offer, on the loose and inconsistent applications of

them, so frequent in the logical phraseology of the

present times.

Sir Isaac Newton himself has, in one of his Que-

ries, fairly brought into comparison the Mathemati-

cal and the Physical AnalysiSy as if the word, in

both cases, conveyed the same idea. " As in Ma-" thematics, so in Natural Philosophy, the investi-

" gation ofdrfficult things, hy the method of ana-

'* lysis, ought ever to precede the method of Com-" position. This analysis consists in making expe-

*' riments and observations, and in drawing conclu-

" sions from them by induction, and admitting of

" no objections against the conclusions, but such as


are taken from experiments, or other certain

truths. For hypotheses are not to i)e regarded

in experimental philosophy. And althotigh the

arguing from experiments and observations by in-

duction be no demonstration of general conclu-

sions;yet it is the best way of arguing which the

nature of things admits of, and may be looked

upon as so much the stronger, by how much the

induction is more general. And if" no exception

occur from phenomena, the conclusion may be

pronounced generally. But if, at any time after-

wards, any exception shall occur from experiments,

it may then begin to be pronounced, with such

exceptions as occur. By this way of analysis we

may proceed from compounds to ingredients ; and

from motions to the forces producing them ; and,

in general, from effects to their causes ; and from

particular causes to more general ones, till the

argument end in the most general. This is the

method of analysis. And the synthesis consists

in assuming the causes discovered, and established

as principles, and by them explaining the pheno-

mena proceeding from them, and proving the ex-

planations." *

It is to the first sentence of this extract (which

has been repeated over and over by subsequent writ-

ers) that I would more particularly request the at-

tention of my readers. Mr Maclaurin, one of the

most illustrious of Newton's followers, has not only

sanctioned it by transcribing it in the words of the

* See the concluding parauraphs of Newton's Optica- ..

388 ELEMENTS OF THE PHILOSOPHY Chap. IV',

author, but has endeavoured to ilkistrate and enforce

the observation whicli it contains. *' It is evident,

" that as in Mathematics, so in Natural Philosophy,

*• the investigation of difficult things by the method*' of analysis ought ever to precede the method of

*' composition, or the synthesis. For, in any other

" way, we can never be sure that we assume the

*' principles which really obtain in nature ; and that

*' our system, after we have composed it with great

*' labour, is not mere dream or illusion." * The

very reason here stated by Mr Maclaurin, one should

liave thought, might have convinced him, that the

parallel between the two kinds of analysis was not

strictly cprrect ; inasmuch as this reason ought, ac-

cording to the logical interpretation of his words, to

bp applicable to the one science as well as to the

other, instead of exclusively applying (as is obvious-

ly the case) to inquiries in Natural Philosophy.

After the explanation which has been already

given of geometrical, and also of physical analysis, it

is almost superfluous to remark, that there is little,

if anything, in which they resemble each other, ex-

cepting this,—that both of them are methods of in-

vestigation and discovery ; and that both happen to

be called by the same name. This name is, indeed,

from its literal or etymological import, very happily

significant of the notions conveyed by it in both in-

stances ; but, notwithstanding this accidental coinci-

dence, the wide and essential difference between the

subjects to which the two kinds of analysis are ap-

* Account of Ne'.Ytou's Discoveries.

Soct. 3. OF THE HUMAN MIND. 389

plied, must render it extremely evident, tliat the ana-

logy of the rules which are adapted to the one can

be of no use in illustrating those which are suited to

the other.

Nor is this all : The meaning conveyed by the

v>ord Analysis, in Physics, in Chemistry, and in

the Philosophy of the Human Mind, is radically

different from that which was annexed to it by the

Greek Geometers, or which ever has been annexed

to it by any class of modern Mathematicians. In

all the former sciences, it naturally suggests the idea

of a decomposition of what is complex into its con-

stituent elements. It is defined by Johnson, *' a se-

" paration of a compound body into the several parts

" of which it consists."—He afterwards mentions,

as another signification of the same word, *' a solu-

" tion of anything, whether corporeal or mental, to

" its first elements ; as of a sentence to the single

*' words ; of a compound word, to the particles and

** words which fonn it 5 of a tune, to single notes ;

"of an argument, to single propositions.'* In the

following sentence, quoted by the same author from

Glanville, the vvord Analysis seems to be used in

a sense precisely coincident with what I have said of

its import, when applied to the Baconian method of

investigation. " We cannot know anytjiing of na-

" ture, but by an analysis of its true initial causes." *

* By the true initial causes of a p/icnomenoii, Glanvil'e moans

(as might be easily shewn by a comparison with other parts of liis

works) t/ie sunple lazvsfrom the cumbination if vchich it results, arul

from a previous knowledge of which, it mJght !;avc been synlhf«i

tically deduced as a consequence.

^90 ELEMENTS OF THE PHILOSOPHY Chap. IV.

Ill tlie Greek geometry, on the other hand, the

same word evidently had its chief reference to the

retrograde direction of this mt thod, when compared

with the natural order of didactic demonstration.

Twj' roiuuinv c'pO'i'oi' ^^says Pappus) aroiAvaLv rcaAawei',

DiGv oLva.irrx.Xiv hvaiv *, a passage which Halley thus

translates : Ii-ic processus Analjjsis vocatur, quasi

dicas, inversa solutio. That this is the primitive and

genuine import of the preposition a i a, is very gener-

ally admitted by Grammarians ; and it accords, in

the present instance, so happily with the sense of the

context, as to throw a new and strong light on the

justness of their opinion. *

In farther proof of what I have here stated with

That Bacon, when he speaks of those separations of nature, hj

means of comparisons, exclusions, and rejections, which form essen-

tial steps in tl.e inductive process, had a view to the analytical

operations of the chemical laboratory, appears sufficiently from

the following words, before quott d :" Itaque naturae facienda

" est prorsus solutio el separaiio ; non per ignem certe, sed per

" mentcm, tanquam ignem divinum."

* The force of this preposition, in its primitive sense, may per-

haps, without any false refinement, be traced more or less palpa-

bly, in every instance to which the word analysis is with any pro-

priety applied. In what Johnson calls (for example) " the sepa-

" ration of* a compound body into the several parts of which it

" consists,"—we proceed on the supposition, that these parts have

previously been combined, or put together, so as to make up the

aggregate whole, submitted to the examination of the chemist;

and, consequently, that the analytic process follows an inverted

or retrograde direction, in respect of that in which the compound

is conceived to have been originally formed.—A similar remark

will be found to apply (mutatis mutandis) to other cases, how-

ever apparently different.

1

|§ect. 3. OF THE HUMAN MIND. 391

respect to the double meaning of the words analysis

and si/nthesLs, as employed in physics and in mathe-

matics, it may not be superfluous to add the follow-

ing considerations. In mathematical analysis, we al-

ways set out from a hypothetical assumption, and our

object is to arrive at some known truth, or some da-

fmn, by reasoning synthetically from which we may

afterwards return, on our own footsteps, to the point

where our investigation began. In all such cases,

the synthesis is infallibly obtained by reversing the

analytical process ; and as both of them liave in view^

the demonstration of the same theorem, or the solu-

tion of the same problem, they form, in reality, but

different parts of one and the same investigation.

But in natural philosophy, a synthesis which merely

reversed the analysis would be absurd. On the con-

trary, our analysis necessarily sets out from known

Jacts; and after it has conducted us to a general prin-

ciple, the synthetical reasoning which follows con-

sists always of an application of this principle to

phenomena, different from those comprehended in

the original induction.

In some cases, the natural philosopher uses theword

Analysis, where it is probable that a Greek geometer

would have used the word Synthesis. Thus, in astro-

nomy, when we attempt from the known phenome-

na to establish the truth of the Copernican system,

we are said to proceed analytically. But the analo-

gy of ancient geometry would apply this word to a

process directly the reverse ; a process which, assum-

ing the system as true, should reason from it to the

known phenomena: Alter which, if the process


coukl be so reversed as to prove that this system, aind

this system alone, is consistent with these facts, it

would bear some analogy to a geometrical synthesis.

These observations had occurred to me, long be-

i'ore I had remarked, that the celebrated Dr Hooke

(guided also by what he conceived to be the analogy

of the Greek geometry) uses the words analysis and

synthesis in physics, precisely in the contrary accep-

tations to those assigned to them in the definitions

of Sir Isaac Newton. " The methods," he observes,

^' of attaining a knowledge in nature may be two ;

" either the analytic or the synthetic. The first is

*' the proceeding from the causes to the effects. The*' second, from the effects to the causes. The for-

*' mer is the morfe difficult, and supposes the thing

*' to be already done and known, which is the thing

" sought and to be found out. This begins from

" the highest, most general and universal principles

" or causes of things, and branches itself out into the

*' more particular and subordinate. The second is the

*' more proper for experimental inquiry, which, from

** a true information of the effect by a due process,

'* finds out the immediate cause thereof, and so pro-

" ceeds gradually to higher and more remote causes

" and powers effective, founding its steps upon the

*' lowest and more immediate conclusions." *

* lioiike's Poblhumous Works, p. 330.

As this volume is now become extremely rare, I shall trans-

cribe the jiarai^raph which immcdiutoly follows the above quota-

tion.

'' An inquisition by the former (or analytic) method, is resem-

" bled litiy enougli by the example of an architect, who hath a


That Hooke was led into this mode of speaking by

the phraseology of the ancient mathematicians, may,

** full comprehension of what he designs to do, and acts accord-

" ingly : But the latter (or synthetic) is more properly resembled

* to that of a husbandman or gardener, who prepares his ground,

*' and sows his seed, and diligently cherishes the growing vcgtta-

*' ble, supplying it continually with fitting moisture, food, and

** shelter,—gbserving and cherishing its continual progression,

" till it comes to its perfect ripeness and maturity, and yields him.

*' the fruit of his labour. Nor is it to be expected, that a pro-

" duction of such perfection as this is designed, should be brought

*' to its complete ripeness in an instant; but as all the works of

** nature, if it be naturally proceeded with, it must have its due

" time to acquire its due form and full maturity, by gradual

" growth and a natural progression ; not but that the other me-

" thod is also of excellent and necessary use, and will very often

" facilitate and hasten the progress. An instance of which kind

*' I designed, some years since, to have given this honourable

" society, in some of my lectures upon the motions and influen-

" ces of the celestial bodies, if it had been then fit ; but I under-

" stand, the same thing will now be shortly done by Mr Newton,

" in a Treatise of his now in the press : But that will not be the

" only instance of that kind which I design to produce, for that I

*' haTe diverse instances of the like nature, wherein, from a hy.

" pothesis being supposed, on a premeditated design, all the phe-

*' nomena of the subject will be a priori foretold, and the eflects

" naturally follow, as proceeding from a cause so and so qualifi-

*• ed and limited. And^ in truth, the synthetic way, by experi'

" ments and observations, will be very sloxo, if it be fiot often assist-

" ed by the analytic, zvhich proves of' excellent me, even though

** it proceed by afalse position ; for that the discovery of a nega-

" live is one way of restraining and limiting an affirjnative."

Change the places of the words analytic and synthetic in this

last sentence, and the remark coincides exactly with what Bosco-

Tich, Hartley, Le Sage, and many other authors, have advanced

in favour of synthetical explanations from hypothcticjil theories.

I shall have occasion afterwards to offer some additional sugges-

39'i ELEMENTS OF THE PHILOSOPHY Chap. IV.

I think, be safely inferred from the following very

sagacious and fortunate conjecture, with respect to

the nature of their analytical investigations, which oc-

curs in a different part of the same volume I do

not know that anything approaching to it is to be

found in the works of any other English author

prior to Dr Halley.

" What ways the ancients had for finding out

" these mediums, or means of performing the thing

" required, we are much in the dark ; nor do any

" of them shew the way, or so much as relate that

" they had such a one : Yet 'tis believed, they were

*' not ignorant of some kind of algebra, by which

" they had a certain way to help themselves in their

*' inquiries, though that we now use be much con-

" fined and limited to a few media. But I do ra-

" ther conceive, that they had another kind of ana-

" lytics, which went backwards through almost all

" the same steps by which their demonstrations went

^'forxvards, though of thiswe have no certain account,

" their writings being altogether silent on that par-

" ticular. However, that such a way is practicable,

" I may hereafter, upon some other occasion, shew

*' by some examples j whereby it will plainly appear,

*' how much more useful it is for the finding out

" the ways for the solution of problems, than that

" which is now generally known and practised by

** species.''**

tions in support of their opinion, and to point out the limitations

which it seems to require.

* llooke's Post. Works, p. 6^.

Of the illuslralions here promised by Hooke of the utility of


The foregoing remarks, although rather of a cri-

tical than of a philosophical nature, may, I hope, be

of some use in giving a little more precision to our

notions on this important subject. They are intro-

duced here, not with the most distant view to any

alteration in our established language (which, in the

present instance, appears to me to be not only unex-

ceptionable, but very happily significant of its true

logical import), but merely to illustrate the occasion-

al influence of words over the most powerful under-

standingsJand the vagueness of the reasonings into

which they may insensibly be betrayed, by a careless

employment of indefinite and ambiguous terms.

If the task were not ungrateful, it would be easy

to produce numerous examples of this from writers

of the highest and most deserved reputation in the

present times. I must not, however, pass over

in silence the name of Condillac, who has certainly

contributed, more than any other individual, to the

prevalence of the logical errors now under consider-

ation. " I know well," says he, on one occasion,"

" that it is customary to distinguish different kinds

" of analysis ; the logical analysis, the metaphysi-

" cal, and the mathematical j but there is, in fact,

the analytical method in geometrical investigations, no traces, as

far as I have observed, occur in his writings. And it would ap.

pear from the following note by the editor, on the passage last

quoted, that nothing important oji the subject had been discover-

ed among his papers.

" 1 do not anywhere find, that this was ever done by Dr Hooke," and leave the usefulness therefore to be considered by the learn-

" ed."

39Q ELEMENTS OF THE PHILOSOPHY Chap. IV.

•* only one analysis ; and it is the same in all the

" sciences.'* * On another occasion, after quoting

from the logic of Port Royal a passage in which it

is said, " That analysis and synthesis differ from

*' each other only, as the road we follow in ascend-

** ing from the valley to the mountain, differs from

" the road by which we descend from the mountaia

" into the valley,"—Condillac proceeds thus :

" From this comparison, all I learn is. That the

*' two methods are contrary to one another, and

" consequently, that if the one be good, the other

** must be bad. In truth, we cannot proceed other-

" wise than from the known to the unknown. Now," if the thing unknown be upon the mountain, it

" will never be found by descending into the val-

" ley Jand if it be in the valley, it will not be found

" by ascending the mountain. There cannot,

" therefore, be two contrary roads by which it is to

*' be reached. Such opinions," Condillac adds,

*' do not deserve a more serious criticism." t

To this very extraordinary argument, it is unne-

cessary to offer any reply, after the observations al-

ready made on the analysis and synthesis of the

Greek geometers. In the application of these two

opposite methods to their respective functions, the

theoretical reasoning of Condillac is contradicted by

the universal experience of mathematicians, both

ancient and modern ; and is, indeed, so palpably ab-

surd, as to carry along with it its own refutation, to

* Lu Logiquc, St'conde Paitie, Cha]). vii.

t Ibid. Chap. vi.


the conviction of every person capable of compre-

hending the terms of the question.—Nor would it

be found more conclusive or more intelligible, if ap-

plied to the analysis and synthesis of natural philo-

sophers ; or indeed to these words, in any of the va-

rious acceptations in which they have ever hitherto

been understood. As it is affirmed, however, by

Condillac, that *' there neither is, nor can be, more" than one analysis," a refutation of his reasoning,

drawn from any particular science, is, upon his own

principle, not less conclusive, than if founded on a

detailed examination of the whole circle of human

knowledge. I shall content myself, therefore, on

the present occasion, with a reference to the mathe-

matical illustrations contained in the former part of

this section.

With regard to the notion annexed to this word

by Condillac himself, I am not certain, if, after all

that he has written in explanation of it, I have per-

fectly seized his meaning. *' To analyze," he tells

us, in the beginning of his Logic, *' is nolhing more" than to observe in a SKCcessive order the qualities

" of an object, with the view of giving them in the

*^ mind that simultaneous order in which they co-ex-

" ist." * In illustration of this definition, he pro-

ceeds to remark, That, " although with a sin^^

" gle glance of the eye, a person may discover a

" multitude of objects in an open cliampaign which

*' he has previously surveyed with attention, yet

" that the prospect is nevermore distinct, than when

* La I.cgifjucj Prcmic're Partic-, Chap. \'\,


" it Is circumscribed within narrow bounds, and

" only a small number of objects is taken in at once.

** We always discern with accuracy but a part of

** what we see."

*' The case," he continues, ** is similar with the

" intellectual eye. I have, at the same moment,

" present to it, a great number of the familiar ob-

" jects of my knowledge. I see the whole group,

" but am unable to mark the discriminating quali-

" ties of individuals. To comprehend with dis-

*' tinctness all that offers itself simultaneously to my** view, it is necessary that I should, in the first

" place, decompose the mass ;—in a manner analo-

" gous to that in which a curious observer would

" proceed in decomposing, by successive steps, the

*' co-existent parts of a landscape.—It is neces-

" sary for me, in other words, to analyze my" thoughts." *

The same author afterwards endeavours still far-

ther to unfold his notion of analysis, by comparing

it to the natural procedure of the mind in the ex-

amination of a machine. *' If I wish," says he,

" to understand a machine, I decompose it, in or-

*' der to study separately each of its parts. As** soon as I have an exact idea of them all, and am" in a condition to replace them as they were for-

* Ibifi. In this last paragraph, I have introduced one or

two additional clauses, which seemed to me necessary for con-

veying clearly the author's idea. Those who take the trouble

to compare it with the original, will be satisfied, that, in ventur-

ing on these slight interpolations, I had no wish to misrepresent

Jiis opinion.

Sect. S. OF THE HUMAN MIND. 399

" merly, I have a perfect conception of the ma-

" chine, having both decomposed and recomposed

<' it."*

In all this, I must confess, there seems to me to

be much both of vagueness and of confusion. In

the two first quotations, the word analysis is employ-

ed to denote nothing more than that separation into

parts, which is necessary to bring a very extensive

or a very complicated subject within the grasp of

our faculties ;—a description, certainly, which con-

veys but a very partial and imperfect conception of

that analysis which is represented as the great or-

gan of invention in all the sciences and arts, t " In

the example of the machine, Condillac's language is

somewhat more precise and unequivocal ; but when

examined with attention, will be found to present

an illustration equally foreign to his purpose. This

is the more surprising, as the instance here appeal-

ed to might have been expected to suggest a juster

idea of the method in question, than that which re-

solves into a literal G?e-composition and r<?-composi-

tion of the thing to be analyzed. That a man may

be able to execute both of these manual operations

on a machine, without acquiring any clear compre-

hension of the manner in which it performs its

work, must appear manifest on the slightest reflec-

tion ; nor is it less indisputable, that another per-

son, without disengaging a single wheel, may gain,

* Ibid. Chap. iii.

•f-" Ce qu'on nonime methode d'hivention^ n'l'st autre rliose que

" Tanalyse. C'est elle qui a fait toutcs les dccouvertes ; c'est par'' elle que nous rctrouvcrons tout ce qui a ete trouvt*." Ibjd.


by a process purely intellectual, a complete know-

ledge of the whole contrivance. Indeed, I appre-

hend, that it is in this way alone that the theory of

any complicated machine can be studied ; for it is

not the parts, separately considered, but the due

combination of these parts, which constitutes the

mechanism.* An observer, accordingly, ofcommon

sagacity, is here guided by the logic of nature, to a

species of analysis, bearing as much resemblance to

those of mathematicians and of natural philosophers,

as the very different nature of the cases admits of.

Instead of allowing his eye to wander at large over

the perplexing mazes of such a labyrinth, he begins

by remarking the ultimate effect ; and thence pro-

ceeds to trace backwards, step by step, the series of

intermediate movements by which it is connected

with the vis motrh\ In doing so, there is undoubt-

edly a sort of mental decomposition of the machine,

inasmuch as all its parts are successively considered

in detail ; but it is not this decomposition which

constitutes the analysis. It is the methodical re-

trogtâdation from the mechanical effect to the me-

chanical pow^r. t

If, on any occasion, a literal decomposition of a machine

•should be found necessary, it can only be to obtain a view of some

of its parts, which, in their combined state, are concealed from

obscrvaliono

+ That this circumstance of rctrogradation or inversion, figur-

ed more than any other in the imagination of Pappus, as the

characteristical feature of geometrical analysis, appears indis-

putably from a clause already quoted from the preface to his

7th book ; Tri'J rota'jrr,v ipoov avakuerj xaXsâsv, mv avarraki*

k-jSiv. To say, therefore, as many writers ha\e done, that the


The passages in Condillac to wliidi these eritl-

cisms refer, arc all selected from his Treatise on Lo-

gic, written purposely to establish his favourite doc-

trine with respect to the influence of language upon

thought. The paradoxical conclusions into which

lie himself has been led by an unwarrantable use of

the words Analysis and Synthesis, is one of the most

remarkable instances which the history of modern li-

terature furnishes ofthe truth of his general principle.

Nor does this observation apply mereiy to the pro-

ductions of his more advanced years. In early life,

he distinguished himself by an ingenious work, in

which he professed to trace analytlcaUij the history

of our sensations and perceptions ; and yet, it has

been very justly remarked of late, that all the rea-

sonings contained in it are purely syntheticaL A,very eminent mathematician of the present times has

even gone so far as to mention it "as a model of

^' êowe^rica/ synthesis." * He would, I apprehend,

analysis of a goomctrica] |ii"obloni consists in deeo»ipo6bii>; or iv-

SQhing it in such a maiinor as may Icatl to the discovery of the

composition or synthesis,—is at once to speak vaguely, and to

keep out of view the cardinal principle on which the utility of

the method hinges. There is, indeed, one species of (Jecoi/iposifioii,

exemplified in the Greek geometry ;

—

t/iat whicli has for its ob-

ject to distinguish all the various cases of a general problem

;

but this part of the investigation was so far from being included

by the ancients in their idea of analysis, that they bestowed upon

it an appropriate name of its own ;—the three requisites to a

complete solution being (according to Pappus) avaXuffa/, )^

ew&eivai, ;^ oiooi'^Ksdai zaTa 'Trruffiv,

* M. Lacroix. See the Introduction to his Elements of Geo-

metry

VOL. II. C C


have expressed his idea more correctly, if, instead of

the epithet geometrical, he had employed, on this

occasion, logical or inetajjhijsical ; in both of which

sciences, as was formerly observed, the analytical

and synthetical methods bear a much closer analogy

to the experimental inductions of chemistry and of

physics, than to the abstract and hypothetical inves-

tigations of the geometer.

The abuses of language which have been now un-

der our review, will appear the less wonderful, whenit is considered tliat mathematicians themselves do

not always speak of analysis and synthesis with their

characteristical precision of expression ; the former

^vord being frequently employed to denote tJie mo-

dern calculus, and the latter, the pure geometi-y ofthe ancients. This phraseology, although it has been

repeatedly censured by foreign writers, whose opi-

nions might have been expected to have some weight,

still continues to prevail very generally upon the

Continent. The learned and judicious author of the

History of IVIathematics complained of it more than

fifty years ago ; remarking the impropriety ** of call-

" ing by the name of the synthetic metliod, that

*' which employs no algebraical calculus, and which

" addresses itself to the mind and to the eyes, by

" means of diagrams, and of reasonings expressed at

" full length in ordinary language. It would be

" more exact," he observes farther, *' to call it the

" method of the ancients, which (as is now univer-

*' sally known) virtually supposes, in all its synthc-

*' tical demonstrations, the previous use of analysis.

" As to the algebraical calculus, it is only an abrid^

Sect. 3. OF TfiE HUMAN MIND. 403

" ged manner of expressing a process of mathemati-

" cal reasoning ;—which process may, according to

*' circumstances, be either analytical or synthetical.

" Of the latter, an elementary example occurs in

" the algebraical demonstrations given by some edi-

" tors of Euclid, of the propositions in his second

« Book." *

This misapplication of the words analysis and syn-

thesis is not, indeed, attended with any serious in-

conveniences, similar to the errors occasioned by the

loose phraseology of Condillac. It were surely bet-

ter, however, that mathematicians should cease to

give it the sanction of their authority, as it has an

obvious tendency,—^beside the injustice which it in-

volves to the inestimable remains of Greek geome-

try,—to suggest a totally erroneous theory, with re-

spect to the real grounds of the unrivalled and

transcendent powers possessed by the modeni calcu-

lusy when applied to the more complicated researches

of physics, t

* Histdire des Malhcmatiques, par Moiitucla, Tome Premier,

pp. \75, \76.

I In the ingenious and profound work of INI. De Gerar.do, en-

titled, Des Signes et de I'Art de Penser, consideres dcwi leitr rap-

porls mutuds, there is a very valuable chapter on the Anal3sis

and S3'nthesis of metaphysicians and of geometers. (See Vol. IV.

p. 172.) The view of the subject which I have taken in the fore-

going section, has but little in common with that given by this

excellent philosopher ; but in one or two instances, where we have

both touched upon the same points (particularly in the strictures

upon the logic of Condillac), there is a general coincidence be-

tween our criticisms, which adds nr.uch to my confidence in myQwn conclusions.

401< ELEMENTS OF THE PHILOSOPHY Chap, IV,

Section IV.

The Consideration of the Inductive Logic resumed.

I.

Additional Remarks on the distinction between Ej:-

perience and Analogy.—Of the ground^ afforded

hy the latter for Scientific Inference and Con-

jecture.

In the same manner in which our external senses

are struck with that resemblance between different

individuals which gives rise to a common appellation,

our superior faculties of obseiTation and reasoning,

enable us to trace those more distant and refined si-

militudes which lead us to comprehend different spe-

cies under one common genus. Here, too, the

principles of our nature, already pointed out, dispose

us to extend our conclusions from what is familiar to

what is comparatively unknown ; and to reason from

species to species, as from individual to individual.

In both instances, the logical process of thought is

nearly, if not exactly, the same ; but the commonuse of language has established a verbal distinction

between them ; our most correct writers being ac-

customed (as far as I have been able to observe) to

refer the evidence of our conclusions, in the one

case, to e.vperience^ and in the other to analogy.

The truth is, that the difference between these two

denominations of evidence, when they are accurate-

ly analyzed, appears manifestly to be a difference,

not in klnd^ but merely in degree ; the discrimina-


tive peculiarities of individuals invalidating tlae infe-

rence, as far as it rests on experience solely, as

much as tlie characteristical circumstances which

draw the line between different species and different

geiiera. *

* In these observations on the import of the word a/ialogi/, as

employed in philosophical discussions, it gives me great pleasure

to lind, that I have struck nearly into the same train of thinking

witli i:l. Frevost. I allude more particularly to the following

passage in his Essais dc Philosophic.

" Iê mot Analogic, dans I'origine, n'exprime que la resscm-

" blancc. ^lais I'usage I'applique h. unc ressemblance eloignee

:

*' d'ou vient que les conclusions analogiques sont souvent hasar-

" dees, et ont bcsoin d'etre d^duites avec art. Toutes les fois done

*' que, dans nos raisonnemcns, nous portons des jugemens scm~

" blablcs sur des objets qui n'ont qu'une ressemblance eloignee,

** nous raisonnons analogiqucment. La ressemblance prochaiiiP

" est celle qui fonde la premit^re generalisation, celle qu'oii

" nomme I'espece. On nomme eloignee la ressemblance qui fonde

" les generalisations supericures, c'cst-^-dire, le genre et ses di-

" vers degves. Mais cette deiinition n'est pas rigoureusement

" suivie.

" Quolqu'il en soil, on congoit des cas, cntre lesquels la ressem-

" blance est si parfaite, qu'il ne s'y trouve aucune difference sen-

" sible, si ce n'est celle du tenis et du lieu. Et ii est des cas

*' dans lesquels on apperôit bcaucoup de ressemblance, mais oii

** Ton docouvre aussi quelques differences independantes de la

'• diversite du temps et du lieu. Lorsque nous ferofis un jngc-

" ment general, fonde sur la premiere espece de ressemblance,

*' nous dirons que nous usons de la mvthode d'indiiction. Lorsque

" la seconde espece de ressemblance autorisera nos raisonncmens,

" nous dirons que c'est de la methode d'analogic que nous faisons

" usage. On dit ordinairement que la methode d'induction con-

" clut du particuller au general, et que la methode d'analogift

" concltit du semblable an semblable. Si I'on analyse ces defini-

40(3 ELEMENTS OF THE PHILO!=;OPHY Chap. IV.

This difference in point of degree (it must at the

same time be remembered) leads, where it is great,

to important consequences. In proportion as the re-

semblance between two cases diminishes in the pal-

pable marks which they exhibit to our senses, our

inferences from the one to the other are made with

less and less confidence ; and, therefore, it is perfect-

ly right that we should reason with more caution

from species to species^ than from individual to indi-

vidual of the same kind. In what follows, accord-

ingly, I shall avail myself of the received distinction

between the words experience and analog?/ ; a dis-

tinction which I have hitherto endeavoured to keep

out of view, till I should have an opportunity of ex-

plaining the precise notion which I annex to it. It

would, in truth, be a distinction of important use in

our reasonings, if the common arrangements, instead

of originating, as they have often done, in ignorance

or caprice, had been really the result of an accurate

observation and comparison of particulars. With all

the imperfections of these arrangements, however,

a judicious inquirer will pay so much regard to pre-

vailing habits of thinking, as to distinguish very scru-

pulously what common language refers to experience

from what it refers to analogy, till he has satisfied

himself, by a diligent examination, that the distinc-

tion has, in the instance before him, no foundation

" tions, on verra que nous n'avons fait autre chose que Icur don-

" nei* de la precision."

—

Essais de Philosophie, Tome II. p. 202.

See also the remarks on Induction and Analogy in the four fol-

lowing articles of M. Pievobt's work.

12

Sect. 4. OF THE HUMAN MI^D. 4'07

in triitli. On the other hand, as mankind are much

more disposed to confound things which ought to be

distinguished, than to distinguish things which are

exactly or nearly similar, he will be doubly cautious

in concluding, that all the knowledge which com-

mon language ascribes to experience is equally solid;

or that all the conjectures which it places to the ac-

count of analogy are equally suspicious.

A different idea of the nature of analogy has been

given by some writers of note ; and it cannot be de-

nied, that, in certain instances, it seems to apply

still better than that proposed above. The two ac-

counts, however, if accurately analyzed, would be

found to approach much more nearly than they ap-

pear to do at first sight ; or rather, I am inclined to

think, that the one might be resolved into the other,

without much straining or over refinement. But

this is a question chiefly of speculative curiosity, as

the general remarks which I have now to offer, will

be found to hold with respect to analogy, considered

as a ground of philosophical reasoning, in whatever

manner the word is defined;provided only it be un-

derstood to express some sort of correspondence or

affinity between two subjects, which serves, as a

principle of association or of arrangement, to unite

them together in the mind.

According to Dr Johnson (to whose definition I

allude more particularly at present), analogy proper-

ly means " a resemblance between things with re-

" gard to some circumstances or effects ; as when" learning is said to enlighten the mind ;—that is,

*' to be to the mind what light is to the eye ; by ena-


*' bling it to discover that which was hidden before."

The statement is expressed with a precision and

justness not always to be found in the definitions of

this author ; and it agrees very nearly with the no-

tion of analogy adopted by Dr Ferguson,—that

*' thing's which have no resemblance to each other

" may nevertheless be analogous ; analogy consist-

*' ing in a resemblance or correspondence of rela-

*' tions." * As an illustration of this, Dr Ferguson

mentions the analogy between the fin of a fish and

the wing of a bird ; the fin bearing the same rela-

tion to the water which the wing does to the air.

lliis definition is more particularly luminous, when

applied to the analogies which are the foundation of

the rhetorical figures of metaphor and allusion ; and

it applies also very happily to those which the fancy

delights to trace between the material and the intel-

lectual worlds ; and which (as I have repeatedly ob-

served) are so apt to warp the judgment in specu-

lating concerning the phenomena ofthe human mind.

The pleasure which the fancy receives from the

contemplation of such correspondences, real or sup-

posed, obviously presupposes a certain disparity or

{?o;?/;y/5/ in the natures of the two subjects compared ;

and, therefore, analogy forms an associating prin-

ciple, specifically different from resemblance, into

^vhich Mr Hume's theory would lead us to resolve

it. An additional proof of this is furnished by the

i'ollowing consideration, That a resemblance of ob-

jects or events is perceived by sensCy and, according-

*" Principli's o[ Moral and Political Science. Vol. I. p. 107-


ly, has some effect even on the lower anhnals ; a co?^-

respondence (or, as it is frequently called, a resem-

blance) of relations^ is not the object of sense, but

of intellecty and, consequently, the perception of it

implies the exercise of reason.

Notwithstanding, however, the radical distinction

between the notions expressed by the words resem-

blance and analogy, they may often approach very

nearly to each other in their meaning ; and cases

may even be conceived in which they exactly agree.

In proof of this, it is sufficient to remark, that in

objects, the parts of which respectively exhibit that

correspondence which is usually distinguished by the

epithet analogous^ this correspondence always de-

viates, less or more, from an exact conformity or

identity ; insomuch, that it sometimes requires a

good deal of consideration to trace in detail the pa-

rallel circumstances, under the disguises which they

borrow from their diversified combinations. An ob-

vious instance of this occurs when we attempt to

compare the bones and joints in the leg and foot of

a man with those in the leg and foot of a horse.

Were the correspondence in all the relations per-

fectly exact, the resemblance between the two ob-

jects would be manifest even to sense j in the very

same manner that, in geometry, the similitude of

two triangles is a necessary consequence of a precise

correspondence in the relatio7is of their homologous

sides.*

This last observation may serve, in some measure,

* See Note (Q.)


to justify an assertion which was already hazarded,

—That the two definitions of analogy formerly men-

tioned are veiy nearly allied to each other j—inas-

much as it shews, by a more careful analysis than has

comm.only been applied to this subject, that the sen-

sible dissimilitude between things of different species

arises chiefly from the want of a palpable conformi-

ty in the relations of their constituent parts. Con-

ceive that more remote correspondence which rea-

son or fancy traces between the parts of the one and

the parts of the other, gradually to approach, nearer

and neai-er, to the same standard ; and it is evident,

that, in the course of the approximation, you will ar-

rive at that degree of manifest resemblance, which

will bring them under the same generic name ; till

at last, by continuing this process of the imagination,

the one will become a correct picture or image of

the other, not only in its great outlines, but in its

minutest details.

From this view of the subject, too, as well as from

the former, it appears how vague and ill-defined the

metaphysical limits are which separate the evidence

of analogy from that of experience ; and how much

room is left for the operation of good sense, and of

habits of scientific research, in appreciating the just-

ness of that authority which, in particular instances,

the popular forms of speech may assign to either.

The illustrations which I have to offer of this last

remark, in so far as it relates to experience, may, I

think, be introduced more usefully afterwards ; but

the vague conceptions which are generally annexed

to the word analogy, together with the prevailing


prejudices against it, as a ground of philosophical

reasoning, render it proper for me, before proceed-

ing any farther, to attempt the correction of some

popular mistakes connected with the use of this ob-

noxious term.

It is not necessary, for the pui-poses which I have

at present In view, to investigate very curiously the

principles which, in the first instance, dispose the

mind to indulge in analogical conjectures from the

known to the unknown. It is sufficient to observe,

that this disposition, so far from being checked, re-

ceives additional encouragement from habits of phi-

losophical study ;—the natural tendency of these ha-

bits being only to guide it into the right path, and

to teach it to proceed cautiously, according to cer-

tain general rules, warranted by experience.

The encouragement which philosophical pursuits

give to this natural disposition, arises chiefly from

the innumerable proofs they afford of that systema-

tical unity and harmony of design which are every-

where conspicuous in the universe. On this unity

of design is founded the most solid argument which

the light of reason supplies for the unity of God ;

but the knowledge of the generalfact on which that

argument proceeds is not confined to the student of

theology. It forces itself irresistibly on the thoughts

of all who are familiarly conversant with the pheno-

mena, either of the material or of the moral world j

and is recognised as a principle of reasoning, even

by those who pay little or no attention to its most

sublime and important application.

It is well known to all who have the slightest ac-


qualntance with the history of medicine, that the

anatomical knowledge of the ancients was derived

almost entirely from analogical conjectures, founded

on the dissection of the lower animals j* and that,

* " If we read the works o( Hippocrates with impartiality,

*' and apply his accounts of the parts to what we 7ioiv know of

" the human body, we must allow his descriptions to be imper-

" feet, incorrect, sometimes extravagant, and often unintelli-

*' gible, that of the bones only excepted. He seems to have

*' studied these with more success than the other parts, and*' tells us, that he had an opportunity of seeing a human" skeleton."

" Erasistratus and Herophilus, two distinguished anatomists

•' at Alexandria, were probably the first who were authorized

'' to dissect human bodies. Their voluminous works are

** all lost ; but they are quoted by Galen, almost in every

" page." . . .

" What Galen principally wanted was opportunities of dis-

" secting human bodies : for his subject was most common-" ]y some quadruped, whose structure was supposed to come" nearest to the human."

" About the year 1540, the great Vesalius appeared. He" was equally laborious in reading the ancients, and in dissect-

" ing bodies ; and in making the comparison, he could not but

" see, that many of Galen's descriptions were erroneous.—The" spirit of opposition and emulation was presently roused, and" many of his contemporaries endeavoured to defend Galen, at

" the expence of Vesalius. In their disputes they made their

*' appeals to the human body : and thus in a few years our art

" was greatly improved. And Vesalius being detected in the

" very fault which he condemns in Galen, to wit, describing

" from the dissections of brutes, and not of the human body,

" it exposed so fully that blunder of the older anatomists, that,

*' in succeeding times, there has been little reason for sucU

" complaint."

Introductory Lectures, delivered by Dr William Hunter to

'Sect. 4. OF THE HUMAN MIND. 413

in consequence of this, many misrepresentations of

facts, and many erroneous theories (blended, how-

ever, with various important truths), were transmit-

ted to the physiologists of modern Europe. Wliat

is the legitimate inference to be deduced from these

premises ? Not, surely, that analogy is an organ of

710 use in the study of nature ; but that, although it

may furnish a rational ground of conjecture and in>

quiry, it ought not to be received as direct evidence,

where the fact itself lies open to examination ; and

that the conclusions to which it leads ought, in every

case, to be distrusted, in proportion as the subjects

compared depart from an exact coincidence in all

their circumstances.

As our knowledge of nature enlarges, we gradu-

ally learn to combine the presumptions arising from

analogy, with other general principles by which they

are limited and corrected. In comparing, for ex-

ample, the anatomy of different tribes of animals, weinvariably find, that the differences in their structure

have a reference to their way of life, and to the ha-

bits for which they are destined ; so that, from

knowing the latter, we might be able, on some oc-

casions, to frame conjectures a imor'i concerning

the former. It is thus, that the form of the teeth,

togetiier with the length and capacity of the intes-

tines, vary in different species, according to the qua-

lity of the food on which the animal is to subsist.

Similar remarks have been made on the different si-

hls last course of anatomjj (London, 1784,) pp. 13, 19,25,

40.

IH ELEMENTS OF THE PHILOSOPHY Chap. IV.

tuation and disposition of the mammWj according as

the animal is uniparous, or produces many at a birth

;

—on the structure and direction of the external ear,

acconling as the animal is rapacious, or depends for

security on his speed ;—on the mechanism of the

pupil of the eye, according as the animal has to

search for his food by day or by night ;—and on va-

rious other organs in the bodily economy, when com-

pared with the functions which they are intended to

perfonn. If, without attending to circumstances of

this sort, a person should reason confidently from

the anatomy of one species to that of another, it can-

not be justly said, that analogy is a deceitful guide,

but that he does not know how to apply analogy to

its proper purpose. In truth, the very consideration

which gives to the argument from analogy its chief

force, points here manifestly to the necessity of

some modification of the original conclusion, suited

to the diversity of the case to which it is to be ap-

plied.

It is remarked by Cuvier, that " a canine tooth,

*' adapted to tear flesh, was never found combined,

** in the same animal, with a hoof, fit for supporting

" the weight of the body, but totally useless as a

" weapon to a beast of prey.'*—" Hence,'* he ob-

serves, " the rule that every hoofed animal is her-

" bivorous ;—and hence (as corollaries from this ge-

" neral principle) the maxims that a hoofed foot in-

*' dicates grinding teeth with flat surfaces, a long

" alimentary canal, a large stomach, and often more*' stomachs than one, with many other similar con-

f* sequences.


*' The laws which regulate the relations between

" different systems of organs," continues this very

ingenious and sound philosopher, *' have the same** influence on the different parts of the same system,

" and connect together its different modifications,

** by the same necessary principles. In the alimen-

*' tary system, especially, where the parts are large

*' and numerous, these rules have their most strik-

" ing applications. The form of the teeth, the

** length, the convolutions, the dilatations of the ali-

" mentary canal, the number and abundance of the

" gastric liquors, are in the most exact adaptation to

*' one another, and have similar fixed relations to

*' the chemical composition, to the solid aggrega-

*' tion, and to the solubility of the aliment ; inso-

*' much that, from seeing one of the parts by itself,

" an experienced observer could foxm conclusions

" tolerably accurate, with respect to the conforma-

" tion of the othei- parts of tlie same system, and*' might even hazard more than random conjectures

*« with respect to the organs of other functions.

" The same harmony subsists among the differ-

" ent parts of the system of organs of motion. As*' all the parts of this system act mutually, and are

*' acted upon, especially when the whole body of the

*' animal is in motion, the forms of all the different

" parts are strictly related. There is hardly a bone

" that can vaiy in its surfaces, in its curvatures, in

*' its protuberances, without corresponding variations

" in other bones ; and in this way, a skilful natural-

" ist, from the appearance of a single bone, will be

^' often able to conclude, to a certain extent, with


" respeet to the form of the whole skeleton to which

" it belonged.

" These laws of co-existence," Cuvier adds,

*^ which have just been indicated, are deduced by" reasoning from our knowledge of the reciprocal in-

*' fluence of the functions, and of the uses of the

"' different organs of the body. Having confirmed

" them by observation, we are enabled, in other cir-

" cumstances, to follow a contrary route ; and,*' wh en we discover constant relations of form be-

*" tween particular organs, we may safely conclude,

" that they exercise some action upon one another

;

" and we may thus be frequently led to form just

" conjectures with respect to their uses.—It is, in-

*' deed, chiefly from the attentive study of these re-

" lations, and from the discovery of relations which" have hitherto escaped our notice, that physiology

" has reason to hope for the extension of her limits

;

*' and, accordingly, the comparative anatomy of ani-

*' mals is to her one of the most fruitful sources of

" valuable discovery." *

The general result of these excellent observations

is, that the improvement of physiology is to be ex-

pected chiefly from lights furnished by analogy;

but that, in order to follow this guide with safety, a

cautious and refined logic is still more necessary

than in conducting those reasonings which rest on

th e direct evidence of experience. When the an-

* See the Introduction to the Lemons d'Anatomic Comparce

de G. Cuvier. The above translation is taken from a very in-

teresting tract, entitled, An Introduction to the Study of the

Animal Economy. (Edinburgh, 1801.)


cient anatomists, without any examination of the

facts witliin their reach, or any consideration of the

peculiaa* functions likely to be connected with man's

erect form and rational faculties, drew inferences

concerning his internal frame, merely from the

structure of the quadrupeds ; the errors into which

they fell,—so far from affording any solid argument

against the use of analogy when judiciously employ-

ed,—have only pointed out to their successors the

necessity of a more discriminating and enlightened

application of it in future ; and have ultimately led

to the discovery of those comprehensive Laws of the

Animal Economy, which, by reconciling apparent

anomalies with the consistency and harmony of one

grand design, open, at every successive step of our

progress, more enlarged and pleasing views of the

beneficent wisdom of Nature.

This speculation might be carried farther, by ex-

tending it to the various analogies which exist be-

tween the Animal and the Vegetable kingdoms, con-

trasted with those characteristical peculiarities by

which they are respectively adapted to the purposes

for which they are destined. It is, however, of

more consequence, on the present occasion, to turn

our attention to the analogies observable among

many of the physical processes by which different

effects are accomplished, or diflerent phenomena pro-

duced, in the system of inanimate and unorganized

matter. Of the existence of such analogies, a sa-

tisfactory proof may be derived from the acknow-

ledged tendency of philosophical habits and scienti-

voL. ir. D d

418 ELEMENTS OF THE PHILOSOPHY Chap. IV*.

fic pursuits, to familiarize the mind with the order

of nature, and to improve its penetration in antici-

pating future discoveries. A man conversant with

physics and chemistry is much more likely than a

stranger to these studies to form probable conjec-

tures concerning those laws of nature which still re-

main to be examined. There is a certain character

or style (if I may use the expression) in the opera-

tions of Divine Wisdom ;—something which every-

where announces, amidst an infinite variety of de-

tail, an inimitable unity and harmony of design j

and in the perception of which, philosophical saga*

city and genius seem chiefly to consist. It is this

which bestows a value so inestimable on the Queries

of Newton. *

* How very deeply Newton's mind was impressed with those

ideas of analogy which I have here ventured to ascribe to him,

appears from his own words. *' Have not the same particles of

'* bodies certain powers, virtues, or forces, by which they act at

" a distance, not only upon the rays of light for reflecting, re-

" fracting, and inflecting them, but also upon one another, for

*' producing a great part of the phenomena of nature ? For it is

" well known that bodies act one upon another, by the attrac-

'' tions of gravity, magnetism, and electricity ; and these in-

*' stafices shew the tenor and course of nature^ and make it not

" improbable but that there may he more attractive poxuers than

*' these. For nature is very consonant and conformable to her--

" self,''' See the 31st Query, at the end of his Optics.

In a subsequent part of this Query, he recurs to the same

principle. *' And thus Nature mil be very conformable to her-

" selfand very simple ; performing all the great motions of the

" heavenly bodies by the attraction of gravity, which intercedes

" those bodies ; and almost all the small ones of their particles,

" some other attractive and repelling powers, which intercede

*' the particles." 1«

Sect. 4. OF THE HUMAN MIND. 41§

This view of the numberless analogies displayed

in that part of the universe which falls under our

immediate notice, becomes more particularly im-

pressive, when it is considered that the same unity

of design may be distinctly traced, as far as the phy-

sical researches of astronomers have extended. In

the knowledge of this fact, we possess important

moral lights, for which we are entirely indebted to

the Newtonian school ; the universal creed of anti-

quity having assumed as a principle, that the celes-

tial phenomena are, in their nature and laws, essen-

tially different from the terrestrial. The Persian

Magi, indeed, are said to have laid down, as one of

their maxims,—5-uiu.7rcc6)i eivuci to, (x.vco tqh -jccctco ;—but that no maxim could stand in more direct oppo-

sition to the tenets of the Grecian philosophers, ap-

pears sufficiently from the general strain of their phy-

sical and astronomical theories. The modern dis-

coveries have shewn, with demonstrative evidence,

how widely, in this fundamental assumption, these

philosophers erred from the truth ; and, indeed, it

was a conjecture a ^jr/or/, originating in some de-

gree of scepticism with respect to it, that led the

way to the doctrine of gravitation. Every subse-

quent step which has been gained in astronomical

science has tended more and more to illustrate the

sagacity of those views by which Newton was guided

to this fortunate anticipation of the truth ; as well

as to confirm, upon a scale which continually grows

in its magnitude, the justness of that magnificent

conception of uniform design, which emboldened


him to connect the physics of the Earth with the

hitherto unexplored mysteries of the Heavens.

Instructive and interesting, however, as these

physical speculations may be, it is still more pleas-

ing to trace the uniformity of design which is dis-

played in the economy of sensitive beings ; to com-

pare the arts of human life with the instincts of the

brutes, and the instincts of the different tribes of

brutes with each other ; and to remark, amidst the

astonishing variety of means which are employed to

accomplish the same ends, a certain analogy charac-

terize them all ;—or to observe, in the minds of dif-

ferent individuals of our own species, the workings

of the same affections and passions, manifesting, a-

mong men of every age and of every country, the

kindred features of humanity. It is this which gives

the great charm to what we call Nature in epic and

dramatic composition,—when the poet speaks a lan-

guage *' to which every heart is an echo," and

which, amidst the manifold effects of education and

fashion, in modifying and disguising the principles

of our constitution, reminds all the various classes

of readers or of spectators of the existence of those

moral ties which unite them to each other, and to

their common parent. *

Nor is it only in the material and moral worlds,

when considered as separate and independent sys-

tems, that this unity of design is perceptible. They

mutually bear to each other numberless relatio?is,

which are more particularly remarkable, when we

* (.Outlines of Moral Philosophy, pp. l.QS, 199, 3d edit.

Scot. 4. OF THE HUMAN MIND. 421

consider both, in their combined tendencies with re-

spect to human happiness and improvement. There

is also a more general analogy, which these two

grand departments of nature exhibit, in the laX€S by

which their phenomena are regulated, and a conse-

quent analogy between the methods of investigation

peculiarly applicable to each. I have already re-

peatedly taken notice of the erroneous conclusions

to which we are liable, when we reason directly from

the one to the other ; or substitute the fanciful ana-

logies between them, which language occasionally

suggests, as a philosophical explanation of the phe-

nomena of either. But it does not follow from this,

that there is no analogy between the rules of inqui-

ry, according to which they are to be studied . Onthe contrary, it is from the principles of inductive

philosophising, which are applicable to both in com-

mon, that we infer the necessity of resting our con-

clusions in each, upon its own appropriate pheno-

mena.

I shall only add, to what has been now stated on

the head of analogy, that the numberless references

and dependencies between the material and the mo-

ral worlds, exhibited within the narrow sphere of our

observation on this globe, encourage, and even au-

thorize us to conclude, that they both form parts of

one and the same plan ;—a conclusion congenial to

the best and noblest principles of our nature, and

which all the discoveries ofgenuine science unite in

confirming. Nothing, indeed, could be more in-

consistent with that irresistible disposition which

prompts every philosophical inquirer to argue from


the known to the unknown, than to suppose that,

while all the different bodies which compose the ma-

terial universe are manifestly related to each other,

as parts of a connected wltolCy the moral events

which happen on our planet are quite insulated ; and

that the rational beings who inhabit it, and for whomwe may reasonably presume it was brought into ex-

istence, have no relation whatever to other intelli-

gent and moral natures. The presumption unques-

tionably is, that there is one great moral system^

corresponding to the material system ; and that the

connections which we at present trace so distinctly

among the sensible objects composing the one, are ex-

hibited as so many intimations of some vast scheme,

comprehending all the intelligent beings who com-

pose the other. In this argument, as well as in

numberless others, which analogy suggests in favour

of our future prospects, the evidence is precisely of

the same sort with that which first encouraged New-

ton to extend his physical speculations beyond the

limits of the Earth. The sole difference is, that he

had an opportunity of verifying the results of his

conjectures by an appeal to sensible facts : but this

accidental circumstance (although it certainly af-

fords peculiar satisfaction and conviction to the as-

tronomer's mind) does not affect the grounds on

which the conjecture was originally formed, and

only furnishes an experimental proof of the justness

of the principles on which it proceeded. Were it

not, however, for the palpable confirmation thus ob-

tained of the Theory of Gravity, it would be diffi-

cult to vindicate, against the charge ofpresumption,


the mathematical accuracy with which the New-tonians pretend to compute the motions, distances,

and magnitudes of worlds, apparently so far remov-

ed beyond the examination of our faculties. *

* ** I know no author," says Dr Reid, " who has made a inore

** just and a more happy use of analogical reasoning than Bi-

" shop Butler, in his Analogy of Religion, Natural and Reveal-

" ed, to the Constitution and Course of Nature. In that exceU*' lent work, the author does not ground any of the truths of re-

** ligion upon Analogy, as their proper evidence. He only makes" use of Analogy to answer objections against them. When" objections are made against the truths of religion, which may" be made with equal strength against what we know to be true

*' in the course of nature, such objections can have no weight,'*

•Êssaj/s on the Intell. Powers, p. 54.

To the same purpose it is observed by Dr Campbell, tha^

" analogical evidence is generally more successful in silencing

" objections than in evincing truth. Though it rarely refutes,

" it frequently repels refutation ; like those weapons which, ^

" though they cannot kill the enemy, will ward his blows."—

Phil. ofRhet. Vol. I. p. 145.

This estimate of the force of analogical reasoning, considered

as a weapon of controversy, is discriminating and judicious.

The occasion on which the logician wields it to the best advan»

tage is, undoubtedly, in repelling the objections of an adversary.

But after the foregoing observations, I may be permitted to ex-

press my doubts, whether both of these ingenious writers have

not somewhat underrated the importance of analogy as a me-

dium of proof, and as a source of new information.— I acknow-

ledge, at the same time, that between the positive and the ne-

gative applications of this species of evidence, there is an essen-

tial difference. When employed to refute an objection, it may

often furnish an argument irresistibly and unanswerably convin«

cing : when employed as a medium of proof, it can never autho=

rize more than a probable conjecture, inviting and encouraging

farther examination. In some instance?, however, the probab!=

iM ELEMENTS or THE PHTLOSOPHY Chat3. I\'.

The foregoing observations have a close connec-.

tion with some reasonings hereafter to be offered in

defence of the doctrine of Jinal causes, Ihey also

throw additional light on what was remarked in a

fonner chapter concerning the unitij of truth ;—

a

most important fact in the theory of the human

mind, and a fact which must strike every candid in^

quirer with increasing evidence, in proportion to the

progress which he makes in the interpretation of

Nature. Hence the effect of philosophical habits

in animating the curiosity, and in guiding the in-

ventive powers ; and hence the growing confidence

which they inspire in the ever consistent and har-

monious conclusions of inductive science. It is

chiefly (as Bacon has observed) from partial and de-

sultory researches that scepticism arises ; not only as

such researches suggest doubts which a more en-

larged acquaintance with the universe would dispel,

but as they withdraw the attention from those com-

prehensive views which combine into a symmetrical

fabric—all whose parts mutually lend to each other

support and stability—the most remote, and seem-

ingly the most unconnected discoveries. " Etenim" symmetria scientice, singulis scilicet partibus se

" invicem sustinentibuSy est, et esse debet, vera at-

" que expedita ratio refellendi cbjectiones minorum*' gentium : Contra, si singula axiomata, tanquam

** baculos fascis seorsim extrahas, facile crit ea in-

" firmare, et pro libito, aut flectere, aut frangere.

lity resulting from a concurrence of different analogies may rise

so high, as to produce an effect on the belief scarcely distinguish-

able from moral certainty. JO


" Num non in aula spatiosa consultius foret, imum" accendere cereum, aut lychnuchum suspendere,

** variis luminibus instructum, quo omnia simul per-

" lustrentur, quam in singulos angulos quaquaver-

*' sus exiguam circumferre lucernam ?'* *

II.

Use and Abuse ofHypotheses in Philosophical In-

quiries,—Differeiice between Gratuitous Hypo-theses, and those which are supported by pre-

sumptions suggested by Analogy,—Indirect Evi-

dence which a Hypothesis may derive from its

agreement with the Phenomena.—Cautions a-

gainst contending some of these conclusions to the

Philosophy of the Human MiJid.

As some of the reasonings in the fonner part of

this Section may, at first sight, appear more favour-

able to the use of Hypotheses than is consistent

with the severe rules of the Inductive Logic, it may

not be superfluous to guard against any such misap-

prehensions of my meaning, by subjoining a few mis-

cellaneous remarks and illustrations.

The indiscriminate zeal against hypotheses, so ge-

nerally avowed at present by the professed followers

of Bacon, has been much encouraged by the strong

and decided terms in which, on various occasions,

they are reprobated by Newton, t But the lan-

* De Augment. Scient. Lib. i.

f " Hypotheses non fingo. Quicquid enim ex phenomenis non

" deducitur hypothesis vocanda est, et hypotheses, seu raetaphy-


guage of this great man, when he happens to touch

upon logical questions, must not always be too liter-

ally intei-preted. It must be qualified and limited,

so as to accord with the exemplifications which he

himself has given of his general rules. Of the

truth of this remark, the passages now alluded to

afford a satisfactory proof ; for, while they are ex-

pressed in the most unconditional and absolute

terms, so many exceptions to them occur in his own

writings, as to authorize the conclusion, that he ex-

pected his readers would of themselves be able to

supply the obvious and necessary comments. It is

probable that, in these passages, he had more parti-

cularly in his eye the Vortices of Descartes.

" The votaries of hypotheses,'* says Dr Reid,

" have often been challenged to shew one useful

" discovery in the works of nature that was ever

** made in that way." * In reply to this challenge,

it is sufficient, on the present occasion, to mention

the theory of Gravitation, and the Copernican sys-

" sicas, seu physicae, seu qualitatum occultarum, seu mechani-

" C£, in philosophia experinientali locum non habcnt." See

tlie general Scholium at the end of the Principia.

* Essays on the Intellectual Powers of Man, p. 88, 4to edit.

In another part of the same volume, the following assertion oc-

curs : " Of all the discoveries that have been made concerning

*' the inward structure of the human body, never one was made" by conjecture. The same thing may be said, with justice,

" of every other part of the works of God, wherein any real dis-

" covery has been made. Such discoveries have always beea

" made by patient observation, by accurate experiments, or by

*' conclusions drawn by strict reasoning from observations and

M experiments ; and such discoveries have always tended to re-


tern. * Of the former, we have the testhtiony of

Dr Pemberton, that it took its first rise from a con-

jecture or hypothesis suggested by analogy ; nor,

indeed, could it be considered in any other light,

till that period in Newton's life, when, by a calcula-

tion founded on the accurate measurement of. the

earth by Picard, he evinced the coincidence between

the law which regulates the fall of heavy bodies, and

the power which retains the Moon in her orbit.

The Copernican system, however, furnishes a case

still stronger, and still more directly applicable to

our purpose ; inasmuch as the only evidence which

the author was able to offer in its favour, was the

advantage which it possessed over every other hy-

pothesis, in explaining with simplicity and beauty

all the phenomena of the heavens. In the mind of

Copernicus, therefore, this system was nothing more

than a hypothesis ;—^but it was a hypothesis conform-

able to the universal analogy of nature, always ac-

complishing her ends by the simplest means. " C*est

" pour la simplicite" says Bailly, " que Copernic

" repla9a le soleil au centre du monde ; c*est pour

" elle que Kepler va detruire tous les epicycles que

" Copernic avoit laisses subsister : pen deprincipes,

" de grands moyens en petit nombre, des phenome-" nes infinis et varies, voila le tableau de I'uni-

** vers." t

*' iute, but not to confirm, the theories and hypotheses which iu-

" genious men had invented."—Ibid. p. 49.

* See Note (R.)

t Histoire de I'Astronomie INIoderne, Tome II. p. 2.

From this anticipation of simplicity in the laub of nature (a


According to this view of the subject, the con-

fidence which we repose in Analogy rests ultimate-

logical principle not less/ universally recognised among ancient

than among modern philosophers), Bailly h.is drawn an argu-

ment^ in support of his favourite hypothesis concerning the ori-

gin of the sciences. His words are these :'' La simplicite n'est

*' pas essentiellement un principe, un axiome, c'est le resultat

** des travaux ; ce n'est pas une idee de I'enfance du monde, elle

" apparticnt h, la maturite des hommes ; c'est la plus grande des

** veriles que I'observation constante arrjiche k I'illusion des ef-

" fets : ce ne peut ^tre qu'un reste de la science primitive.

" Lorsque chcz un peuple, possesseur d'une niythologie compli-

" qu6e, et qui n'a d'autre physique queces fables, los philosophes,

" voulant reduire la nature a un seul principe, annonceront que

" I'eau est la source de toutes choses, ou le feu I'agent uuiversel,

*' nous dirons h. ces philosophes : vous parlez une langue que*' n'est pas la votre ; vous avez saisi par un instinct philoso«

" phique ces verites au-dessus de votre siecle, de viotre nation, et

*' de vous-memes ; c'est la sagesse des anciens qui vous a etc

" transniise par tradition,'' &c. &c. &c.—Ibid. p. 4.

To the general remark which introduces this passage I readily

subscribe. The confidence with which philosophers anticipate

the simplicity of Nature's laws is unquestionably the result of

experience, and of experience alone; and implies a far more

extensive knowledge of her operations than can be expected from

the uninformed multitude. The inference, however, deduced

from this, by the ingenious and eloquent, but sometimes too fan-

ciful historian, is not a little precipitate. The passion for ex-

cessive simplification, so remarkably exemplified in the physical

systems of the Greeks, seems to be sufficiently accounted for by

their scanty stock of facts, combined with that ambition to ex-

plain everything from the smallest possible number of data, which,

in all ages of the world, has been one of the most common iofir-

mities of genius. On the other band, the principle in questaon,

when stated in the form of a proposition, is of so abstract and

metaphysical a nature, that it is highly improbable it should have

Sect. 4. ,OP THE HUMAN MIND. 4^9

ly on the evidence of Experience ; and hence, an

additional argument in favour of the former method

of investigation, when cautiously followed, as well

as an additional proof of the imperceptible shades by

which Experience and Analogy run into each other.

Nor is the utility of hypothetical theories confined

.to those cases in which they have been confirmed by

subsequent researches : it may be equally great, where

they have completely disappointed the expectations

of their authors. Nothing, I think, can be juster

than Hartley's remark, that " any hypothesis which** possesses a sufficient degree of plausibility to ac-

" count for a number of facts, helps us to digest

" these facts in proper order, to bring new ones to

" light, and to make ea^perhnenta crucis for the

" sake of future inquirers."* Indeed, it has pro-

bably been in this way that most discoveries have

been made ; for, although a knowledge of facts must

be prior to the formation of a legitimate theory,

yet a hypothetical theory is generally the best guide

to the knowledge of connected and of useful facts.

The first conception of a hypothetical theory, it

must always be remembered (if the theory pos-

sesses any plausibility whatever), presupposes a gene-

survived the shock of revolutions which had proved fatal to the

memory of particular discoveries. The arts, it has been fre-

quently observed, are more easily transmitted by mere tradition,

from one generation to another, than the speculative sciences

;

and, for a similar reason, physical systems are far less likely to

sink into oblivion, than abstract maxims, which have no imme-

diate reference to objects of sense, or to the ordinary concerns

of life.

* Observations on Man, Chap. i. Prop. v.

430 ELEMENTS OF THE THILOSOPHY Chap. IV.

ral acquaintance with the phenomena which it

aims to account for; and it is by reasoning syn-

thetically from the hypothesis, and comparing the

deductions with observation and experiment, that

the cautious inquirer is gradually led, either to cor-

rect it in such a manner as to reconcile it with facts,

or finally to abandon it as an unfounded conjecture.

Even in this latter case, an approach is made to the

truth in the way of exclusio7i ; while, at the same

time, an accession is gained to that class of asso-

ciated and kindred phenomena, which it is his object

to trace to their parent stock.*

In thus apologizing for the use of hypotheses, I

only repeat in a different form the precepts of

Bacon, and the comments of some of his most en-

lightened followers. " The prejudice against hy-

" potheses which many people entertain," says the

late Dr Gregory, " is founded on the equivocal sig-

" nification of a word. It is commonly confounded

" with theory ;—^but a hypothesis properly means

" the supposition of a principle of whose existence

" there is no proof from experience, but which may** be rendered more or less probable by facts which

" are neither numerous enough, nor adequate to in-

* " lUud interim monemus; ut nemo animo concidat, aut

*' quasi confundatur, si cxperimenta, quibus incumbit, expec-

" tationi su^ non respondeant. Etenim quod succedit, magis

*' complaceat; at quod non succedit, saipenuraero non minus in-

" format. Atque illud semper in animo tenendum, experimenta

" lucifera etiam adhuc magis, quam fructifcra ambienda esse.

" Atque de literata experimentia hccc dicta sint; qure sagacitas

" potius est, et odoratio quondam venaiica, quam sckntia."-—De

Augm, Scient. Lib. v. Cap. ii«


" fer its existence* When such hypotheses are pro-

" posed in the modest and diffident manner that

'^» becomes mere suppositions or conjectures, they

** are not only harmless, but even necessary for

" establishing a just theory. Thej/ are the Jirst

" rudiments or anticipation of Principles. With-

** out these, there could not be useful observation,

** nor experiment, nor arrangement, because there

" could be no motive or principle in the mind to

«* form them. Hypotheses then only become dan-

** gerous and censurable, when they are imposed on** us for just principles ; because, in that case, they

** put a stop to further inquiry, by leading the mind" to acquiesce in principles which may as probably

" be ill as well founded." *

Another eminent writer has apologized very in-

geniously, and I think very philosophically, for the

hypotheses and conjectures which are occasionally

to be found in his own works. The author I mean

is Dr Stephen Hales, who, in the preface to the

second volume of his Vegetable Statics, has ex-

pressed himself thus

:

" In natural philosophy, we cannot depend on*• any mere speculations of the mind ; we can only

" reason with any tolerable certainty from proper

** data, such as arise from the united testimony of

" many good and credible experiments.

" Yet it seems not unreasonable, on the other

** hand, though not far to indulge, to carry our rea-

** sonings a little farther than the plain evidence of

* I.ectures on the Duties and the Qualifications of a Phy-

:-ician.

432 ELEMENTS QF THE PHILOSOPHY Chap, IV'.

" experiments will warrant ; for since at the ut-

" most boundaries of those things which we clearly

" know, a kind of twilight is cast on the adjoining

" borders of Terra Incognita^ it seems reasonable,

*' in some degree, to indulge conjecture there

;

" otherwise we should make but very slow ad-

" vances, either by experiments or reasoning. For

" new experiments and discoveries usually owe their

" first rise only to lucky guesses and probable con-

" jectures ; and even disappointments in these con-

" jectures often lead to the thing sought for.'*

To these quotations I shall add two short ex-

tracts from Dr Hooke (the contemporary, or rather

the predecessor, of Newton), whose acute and ori-

ginal remarks on this subject reflect the greater

credit on his talents, that they were published at a

period, when the learned body of which he was so

illustrious an ornament, seem plainly to have been

more disposed to follow the letter of some detached

sentences, than to imbibe the general spirit of Ba-

con's logic.

" There may be use of method in the collecting of

" materials, as well as in the employment of them j

" for there ought to be some end and aim ; some

*' predesigned module and theory ; some purpose in

" our experiments. And though this Society have

" hitherto seemed to avoid and prohibit preconceived

" theories and deductions from particular and seeuv

*' ingly accidental experiments ; yet I humbly con-

" ceive, that such, if knowingly and judiciously

*' made, are matters of the greatest importance j as

" giving a characteristic of the aim, use, and sigui-

Sect. 4. OF THE HUMAN MIND. 43S'

" tication thereof; and without which many, and

" possibly the most considerable particulars, are pas-

*' sed over without regard and observation. *

*' Wliere the data on which our ratiocinations are

" founded are uncertain, and only conjectural, the

*' conclusions or deductions therefrom can at best be

" no other than probable, but still they become more*' and more probable, as the consequences deduced*' from them appear, upon examinations by trials and

*' designed observations, to be confirmed by fact or

*' effect. So that the effect is that which consum-*' mates the demonstration of the invention ; and

" the theory is only an assistant to direct such an

" inquisition, as may procure the demonstration of

'* its existence or non-existence." t

As an illustration of this last remark, Hooke men-

tions his anticipation of Jupiter's motion upon his

axis, long before he was able, by means of a good

telescope, to ascertain the fact. A much more re-

markable instance, however, of his philosophical sa-

gacity, occurs in his anticipation of that theory of

the planetary motions, which, soon after, was to pre-

sent itseli", with increased and at length demonstra-

tive evidence, to a still more inventive and powerful

mind. This conjecture (wjiicli I shall state in his

own words) affords, of itself, a decisive reply to the

undistinguishing censures which have so often been

bestowed on the presumptuous vanity of attempting,

* llouke'i. Posthumous Works, j). 280.

t Ibid. p. 337. For another extract from the same workj

see Note (S.)

VOL. II. E e

434* ELEMENTS OF THE PHILOSOPHY 'Cliap. IV'.

by means of hypotheses, to penetrate into the secrets

of nature.

" I will explain (says Hooke, in a connnunication

*' to the Royal Society in KiOti) a system of the

" world very difterent from any yet received. It is

" founded on the three following positions :

'* 1. That all the heavenly bodies have not only

*' a gravitation of their parts to their own proper

*' centre, but that they also mutually attract each

" other within their spheres of action.

*' Q. That all bodies, having a simple motion, will

" continue to move in a straight line, unless con-

" tinually deflected from it by some extraneous

" force, causing them to describe a circle, an ellipse,

" or some other curve.

" 3. That this attraction is so much the greater

" as the bodies are nearer. As to the proportion in

*' which those forces diminish by an increase of dis-

*' tance, I own I have not discovered it, although I

" have made some experiments to this purpose. I

*' leave this to others, who have time and knowledge

'* sufficient for the task.'*

The argument in favour of Hypotheses might be

pushed much farther, by considering the tentative

or IiT/pothetical ste])shy which the most cautious phi-

losophers are often under the necessity of proceed-

ing, in conducting inquiries strictly experimental.

Tliese cannot be better described than in the words

of Boscovich, the slightest of whose logical hints are

entitled to peculiar attention.—" In some instances,

" observations and experiments at once reveal to us

" all that we wish to know. In other cases, we

Sect, 4. OF THE HUMAN MIND. 435

" avail ourselves of the aid o^liypothcses ;—by "oohick

" xvordy however, is to be understood^ not fictions

*' altogether arbitraryy but suppositiojis co?iform-

" able to experience or to analogy. By means of

** these, we are enabled to supply the defects of

*' our data, and to conjecture or divine the path to

" truth Jalways ready to abandon our hypothesis,

" when found to involve consequences inconsistent

" with fact. And, indeed, in most cases, I conceive

" this to be the method best adapted to physics ; a

" science in which the procedure of the inquirer

*' may be compared to that of a person attempting

" to decypher a letter written in a secret character ;

" and in which legitimate theories are generally the

" slow result of disappointed essays, and of errors

" which have led the way to their own detection."*

* De Soil's ac Lunse Defectibus. Lond. 17^0, pp. 21 1, 212.

For the continuation of the above passage, see Note (T.)

INIany remarks to the same purpose may be found in Bacon,

The following happen at present to occur to my memory

:

" Deo (formarum inditori et opifici) et fortasse angelis compe-

" tit, formas per affirraationem immediate nosse, atque ab initio

** contemplationis. Sed certe supra hominem est ; cui tantum

" concedilur, procedere primo per negathas, et postremo loco de-

" sinere in affirmativas, post omnimodam exclusionem. . . .

" . , Post rejectionem et exclusionem debitis modis factam, se-

" cundo loco (tanquam in fundo) manebit(abeuntibusinfumuni

*' opinionibus volatilibus)ybr?wa affirmativa, solida, et vera. At-

" que hoc brevi dictu est, sed per multas ambages ad hoc peiTe^

« mtm:'—Nov. Org. Lib. II. Aphor. XV. XVI.

" Prudens interrogation quasi dimidium scienticC. Idcirco quo

" amplior et certior fuerit anticipatio nostra ; eo magis directa et

" compendiosa erit investigatio."

—

De Aug, Scient, Lib. V,

Cap. 3,

436 ELEMENTS OP THE PHILOSOPHY Chap. I\ .

Nor is it solely by the erroneous results of his own

Jiypotheses, that the philosopher is assisted in the in-

vestigation of truth. Similar lights are often to be

collected from the errors of his predecessors ; and

hence it is, that accurate histories of the different

sciences may justly be ranked among the most effec-

tual means of accelerating their future advancement,

[t was from a review of the endless and hopeless

wanderings of preceding inquirers, that Bacon infer-

red the necessity of" avoiding every beaten track

;

" Vaga experieatia et se tantum scquens mera palpatio est, et

" homines potius stupcfacit, quam informat."

—

Nov. Or^. Lib. I.

Aphor. C.

The reader who wishes to prosecute farther this speculation

concerning: the use of hypotheses, may consult with advantage

three short but interesting memoirs upon Method, by the late M.Le Sage of Geneva, which M. Prevost has annexed as a supple-

ment to his Essais de Philosophie. Tliat I may not be supposed,

however, to acquiesce in all this author's views, I shall mention

two strong objections lo which some of them appear to me to be

liable.

1

.

In treating of the method of Hypothesis, Le Sage uniformly

contrasts it with that of Analogy, as if the two were radically dis-

tinct, and even opposite in their spiiit ; whereas it seems evident,

that some perception of analogy must have given birth to every

hypothesis which possesses a sufficient degree of plausibility to

deserve farther examination.

2. In applying the rules of Mathematical Method to Physics,

he makes far too little allowance for the essential difference be-

tween the two sciences. This is jnore particularly remarkable

in his observations on the aid to be derived, in investigating the

laws of nature, from the method of Exclusions,—so happily em-

ployed by Trcnicle de Bessy (a French mathematician of tlir

seventeenth century) in the solution of some very difficult pro-

blems relating to numbers.—Se(? Note (U.)

Sect. 4, OF THfi HUMAN MIND. 4S7

and it was this which encouraged him—with a con-

fidence in his own powers amply justified by the

event—to explore and to open a new path to the

mysteries of nature : Inveniam viam, aut Jaciam.

In this respect, the maturity of reason in the species

is analogous to that in the individual ; not the con-

sequence of any sudden or accidental cause, but the

fruit of reiterated disappointments correcting the

mistake's of youth and inexperience. " There is no*' subject,'* says Fontenelle, " on which men ever

" come to form a reasonable opinion, till they have

" once exhausted all the absurd views which it is

*' possible to take of it. What follies," he adds,

** should we not be repeating at this day, if we had

*' not been anticipated in so many of them by the

" ancient philosophers I"—Those systems, there-

fore, which are false, are by no means to be regard-

ed as altogether useless. That of Ptolemy (for ex-

ample), as Bailly has well observed, is founded on a

prejudice so natural and so unavoidable, that it may

be considered as a necessary step in the progress of

astronomical science ; and if it had not been propos-

ed in ancient times, it would infallibly have preced-

ed, among the moderns, the system of Copernicus,

and retarded the period of its discovery.

In what I have hitherto said in defence of the

method of Hypothesis, I have confined myself en-

tirely to its utility as an organ of investigation ; tak-

ing all along for granted, that, till the principle as-

sumed has been fairly ini'erred as a law of nature,

from undoubted facts, none of the explanations

which it affords are to be admitted as lesitiraato


theories. Some of the advocates for this method

have, however, gone much farther ; asserting, that

if a hypothesis be sufficient to account for all the

phenomena in question, no other proof of its confor

mity to truth is necessary. *' Supposing," says Dr

Hartley, " the existence of the cviher to be destitute

** of all direct evidence, still, if it serves to explain

** and account for a great variety of phenomena, it

" will, by this means, have an indirect argument in

" its favour. Thus, we admit the key of a cypher

** to be a true one, when it explains the cypher com-

** pletely ; and the decypherer judges himself to ap-

** proach to the true key, in proportion as he advan-

** ces in the explanation of the cypher ; and this

** without any direct evidence at all." * On ano-

ther occasion, he observes, that " Philosophy is the

" art of decypliering the mysteries of nature -, and

" that every theory which can explain all the phe-

" nomena, has the same evidence in its favour, that

" it is possible the key of a cypher can have from its

" explaining that cypher." t

The same very ingenious and plausible reasoning

is urged by Le Sage in one of his posthumous frag-

* Observations on Man, Vol. I. pp. 15, \6. (4th edit.)

+ Ibid. p. 350. The section from which this quotation is

taken (entitled " Of Propositions and the nature of Assent") con-

tains various ingenious and just observations, blended with others

strongly marked with the author's peculiar turn of thinking. A-

mong these last may be mentioned his Theory of Mathematical

Evidence, coinciding exactly with that which has since been

proposed by Dr Beddoes. Compare Hartley with pji. 198. and

199 of this volume.

Scci. 4. OF THE HUMAN MIND. 439

ments ;* and, long before the publication of Hart-

ley's work, it liacl struck Gravesande so strongly,

that, in his Introductio ad Philosophiam, he has

subjoined to his chapter on the Use of Hypotheses,

another on the Art of Decyphering. Of the merit

of the latter it is no slight proof, that D'Alembert

has inserted the substance of it in one of the articles

of the Encijclopedie. t

In reply to Hartley's comparison between the bu-

siness of the philosopher and that of the decypherer,

Dr Keid observes, that *' to find the key requires

'* an undeistanding equal or superior to that which

" made the cypher. This instance, therefore,*' he

adds, " will tlien be in point, when he who attempts

" to decypher the works of nature by a hypothesis,

" has an understanding equal or superior to that

" which made them." X

This argument is not stated with the author's

usual correctness in point of logic j inasmuch as the

tirst proposition contrasts the sagacity of the decy-

pherer with that of the contriver of the cypher ;

and tlie second, with that of the author of the co7n-

position decyphered. Nor is this all. The ajrgu-

* " N'admcttons-nous pas pour viaie, la clef d'une lettrc

" ecrite en chiftVcs, ou cclle d'une logogryphe;quand cqHg clef

" s'applique exactment a tous les caracteres dont il faut rendre

" raison ?"

—

Opuscules dc G. L. Le Sage, relatifs a la Methode.

See M. Prevost's Essais de Philosophie.

\ Article Dechiffrer. See also D'Alembert's Oeuvres Post=

humes. Tome II. p. 177.-—Gravesande's Logic was published

in 1736.

X Essays on the Intell. Powers, p. 88.

440 ELEMENTS OF THE PHILOSOPHY Cliiip. ]\\

ment proceeds on the supposition, that, if the task

of the scientific inquirer be compared to that of the

decypherer, the views of the Author of nature may,

with equal propriety, be compared to those of the-

inventor of the cypher. It is impossible to imagine

that this was Hartley's idea. The object of true

philosophy is, in no case presumptuously to di\ino

an alphabet of secret characters or cyphers, purpose-

ly employed by infinite Wisdom to conceal its ope-

rations ; but, by the diligent study of facts and ana-

logies legible to all, to discover the key which infi-

nite AVisdom has itself prepared for the interpreta-

tion of its own laws. In other words, its object is

to concentrate and to cast on the unknown parts of

the universe, the lights which are reflected from

those which arc known.

In this instance, as well as in others, where Reid

reprobates hypotheses, his reasoning unifoiTnly takes

for granted, that they are wholly arbitrary and gra-

tuitous. " If a thousand of the greatest wits," says

he, " that ever the world produced, were, uithout

*' any previous Jino'u.iedge in anatomy ^ to sit down** and contrive how, and by what internal organs,

" the various functions of the human body are car-

' ried on—^liow the blood is made to circulate, and*' the limbs to move—they would not, in a thou-

*' sand years, hit upon anything like the truth." *

Nothing can be juster than this remark ; but does

it authorize the conclusion, that, to an experienced

and skilful anatomist, conjectures founded on ana-

logy, and on the consideration of useSy are of n«

* Ibid. p. 49.

Sect. 4. OT THE HUMAN MIN». 441

avail as media of discovery ? The logical inference,

indeed, from Dr Reid*s own statement, is not a-

gainst anatomical conjectm'es in general, but against

the anatomical conjectures of those who are ignorant

of anatomy.

The same reply may be made to the following

assertion of D'Alembert ; another writer, who, in

my opinion, has, on various occasions, spoken much

too lightly of analogical conjectures : "It may be

*' safely affirmed, that a mere theorist ('ttn Physi-** cien de Cabinet) who, by means of reasonings and*' calculations, should attempt to divine the pbeno-

*' mena of nature, and who should afterwards com-

" pare his anticipations with facts, would be asto-

" nished to find how wide of the truth almost all of

" them had been." * If this observation be con-

fined to those system-builders who, without any

knowledge of facts, have presumed to form conclu-

sions a 'priori concerning the universe, its truth is

so obvious and indisputable, that it was hardly worth

the while of this profound philosopher so formally

to announce it. If extended to such men as Coper-

nicus, Kepler, and Newton, and to the illustrious

train who have issued from the Newtonian school,

it is contradicted by numberless examples, of which

D*Alembert could not fail to be perfectly aware, t

* Melan cs de Litterature, &c. Tome V. ^ 6. (entitled E-

claircisscmeiit sur ce qui a ele dit, &c. de I'art de conjecturer.)

+ Accordingly, in another part of the same article, he has

said :'< L'analogie, c'est-a-dire, la ressemblance plus on moi/is

" grande des faits, le rapport plus ou moins sensible qu'ils ont

'* enlr'eux, est Tunique regie des physiciens, soit pour expliquer

" les faits connus, soit pour en decouvrir de noyveaux."

4>4s'^ ELEMENTS OP THE PHILOSOPHY Chap. IV.

The sagacity which guides the Philosopher in

conjecturing the laws of nature has, in its metaphy-

sical origin, a veiy near affinity to that acquired

perception of human character, which is possessed

by Men of the World, The conclusions of one in-

dividual with respect to the springs of action in the

breast of another, can never, on the most favourable

supposition, amount to more than to a Hypothesis

supported by strong analogies; yet how different is

the value of the Hypothesis, according to the intel-

lectual habits of him by whom it is formed ! Whatmore absurd and presumptuous than the theories of

the cloistered schoolman concerning the moral or

the political phenomena of active life ! What more

interesting and instructive than the slightest charac-

teristical sketches from the hand of a Sully or of a

Clarendon !

To these suggestions in vindication of hypotheses

it may be added, that some of the reasonings which,

with propriety, were urged against them a century

ago, have already, in consequence of the rapid pro-

gress of knowledge, lost much of their force. It is

very justly remarked by M. Prevost, that " at a pe-

" riod when science has advanced so far as to have

" accumulated an immense treasure of facts, the dan-

" ger of liypotheses is less, and their advantages

*' greater, than in times of comparative ignorance.'*

For this he assigns three reasons. '* 1. The multi-

*' tude of facts restrains Imagination, by presenting,

" in every direction, obstacles to her wanderings;

" and by overturning her frail edifices. 2. In pro-

*' portion as facts multiply, the memory stands in

Sect. 4.'^"' "^"^^ HUarAN MIND.

**ffiêat*^

neeH of the aid of connecting or as-

i( oociating principles. * 3. The chance of disco-

" vering interesting and himinous relations among**^ the objects of our knowledge increases with the

** growing number of the objects compared." t

—

The considerations already stated suggest a 4th rea-

son in confirmation of the same general proposition :

—That, by the e^te?ision of human knowledge, the

scale upon which the Analogies of Nature may be

studied, is so augmented as to strike the most heed-

less eye ; while, by its diffusion^ the perception of

these analogies (so essential an element in the com-

position of inventive genius) is insensibly communi-

cated to all who enjoy the advantages of a liberal

education. Justly, therefore, might Bacon say,

" Certo sciant homines, artes inveniendi solidas et

" veras adolescere et incrementa sumere cum ipsis

** inventis."

But although I do not think that Reid has been

successful in his attempt to refute Hartley* s argu-

ment, I am far from considering that argument as

sound or conclusive. My chief objections to it are

the two following

:

1. The cases compared are by no means parallel.

In that of the cypher, we have all the facts before

us ; and, if the key explains them, we may be cer-

tain that nothing can directly contradict the just-

ness of our interpretation. In our physical research-^

* With respect to the utility of hypothetical theories, as ad-

mimcles to the natural powers of memory, see the former volume

of this work, Chap. vi. Sections 3 and 4.

f See Note (X.)

A

4>4f4> ELEMENTS OF THE PHILo»r,pHY Chan. IV.

eSy on the other hand, we are admitted lo .êe only

a few detached sentences extracted from a voluiao

of the size of which we are entirely ignorant. Nohypothesis, therefore, how numerous soever the facts

may be with which it tallies, can completely exclude

the possibility of exceptions or limitations hitherto

undiscovered.

It must, at the same time, be granted, that the

probability of a hypothesis increases in proportion to

the number of phenomena for which it accounts,

a?id to the simplicitij of the theory by which it ex-

plains them ;—and that, in some instances, this pro-

bability may amount to a moral certainty. Themost remarkable example of this which occurs in the

history of science is, undoubtedly, the Copernican

system. I before observed, that at the period when

it was first proposed, it was nothing more than a hy-

pothesis ; and that its only proof rested on its con-

formity, in point of simplicity, to the general

economy of the Universe. '* When Copernicus,"

says Mr Maclaurin, " considered the form, disposi-

" tion, and motions of the system, as they were then

" represented after Ptolemy, he found the whole

" void of order, symmetry, and proportion ; like a

" piece," as he expresses himself, *' made up of parts

" copied from different originals, which, not fitting

*' each other, should rather represent a monster

" than a man. He therefore perused the writings

*' of the ancient philosophers, to see whether any

" more rational account had ever been proposed of

" the motions of the Heavens. The first hint he

•' had was from Cicero, who tells us, in his Acade-

Sect. 4<. OF THE HUMAN MIND. 445

" mical Questions, that Nicetas, a Syracusian, had

" taught that the earth turns round on its axis,

" which made the whole heavens appear to a spec-

" tator on the earth to turn round it daily. After-

" wards, from Plutarch he found that Philolaus, the

** Pythagorean, had taught that the earth moved an-

" nually round the sun. He immediately perceived,

** that, by allowing these two motions, all the per-

" plexity, disorder, and confusion he had complain-

" ed of in the celestial motions, vanished ; and that,

" instead of these, a simple regular disposition of the

*' orbits, and a harmony of the motions appeared,

" worthy of the great Author of the world,'* *

Of the truth of this hypothesis, the discoveries of

the last century have afforded many new proofs of a

direct and even demonstrative nature ; and yet, it

may be fairly questioned, whether to Copernicus

and Galileo, the analogical reasoning, stated in the

preceding quotation, did not, of itself, appear so con-

clusive, as to supersede the necessity of any farther

evidence. The ecclesiastical persecutions which the

latter encountered in defence of his supposed heresy,

sufficiently evinces the faith which he reposed in his

astronomical creed.

* Account of Newton's Philosophical Discoveries, p. 45. (2d

edit.)

This presumptive argument, as it presented itself to the mind

©f Copernicus, is thus stated by Bailly :" Les hommes sentent

** que la nature est simple ; les stations et les letrogradations des

" planetes offroient des apparences bizarres ; le principe, qui les

** ramenoit h. une marche simple, et naturelle, ne pouvoit etrc

" quune verite.^'-Ûisi. de VJstron. Mod. Tom, I. p. 351.

446 ELEMENTS OF THE PHILOSOPHY Chap. IV

It is, however, extremely worthy of remark, with

respect to the Coperaican system, that it affords no

illustration whatever of the justness of Hartley's lo-

gical maxim. The Ptolemaic system was not de-

monstrably inconsistent with any phenomena known

in the sixteenth century ; and, consequently, the

presumption for the new hypothesis did not arise

from its exclusive coincidence with the facts, but

from the simplicity and beauty which it possessed as

a theory. The inference to be deduced from it is,

therefore, notm favour of hypotheses in general, but

of hypotheses sanctioned by analogy.

The fortunate hypothesis of a Ring encircling the

body of Saturn, by which Huyghens accounted, in a

manner equally simple and satisfactory, for a set of

appearances which, for forty years, had puzzled all

the astronomers of Europe, bears, in all its circum-

stances, a closer resemblance than any other instance

I know of, to the key of a cypher. Of its truth it

is impossible for the most sceptical mind to entertain

any doubt, wlien it is considered, that it not only

enabled Huyghens to explain all the knowm^hGno-

mena, but to predict those which were afterwards to

be observed. This instance, accordingly, has had

much stress laid upon it by different writers, parti-

cularly by Gr^vesande and Le Sage. * I must own,

I am somewhat doubtful, if the discovery of a key to

* Gravesande, IntrocK ad Philosophy §§ ^79> 985.—Opuscules

de Le Saê, Premier Memoire, § 25. The latter writer mentions

the theory in question, as a hypothesis which received no coun-

tenance whatever from the analogy of any preceding astronomical

discovery.

Sect. 4. OF THE HUMAN MIND. M7SO limited and insulated a class of optical fiicts, au-

thorizes any valid argument for the employment of

mere hypotheses, to decypher the complicated pheno-

mena resulting from the general laws of nature. It

is, indeed, an example most ingeniously and happily

selected ; but would not perhaps have been so often

resorted to, if it had been easy to find others of a si-

milar description.

2. The chief objection, however, to Hartley's

comparison of the theorist to the decypherer is, that

there are few, if any, physical hypotheses, which af-

ford the 07ilj/ way of explaining the phenomena to

which they are applied ; and, therefore, admitting

them to be perfectly consistent with all the known

facts, they leave us in the same state of uncertainty,

in which the decypherer would find himself, if he

should discover a variety of keys to the same cypher.

Descartes acknowledges, that the same effect

might, upon the principles of his philosophy, admit

of manifold explanations ; and that nothing perplex-

ed him more than to know which he ought to adopt,

in preference to the others. " The powers of na-

" ture," says he, *' I must confess, are so ample,

" that no sooner do I observe any particular effect;

" than I immediately perceive that it may be de-

" duced from w?/ principles, in a variety of different

" ways ; and nothing, in general, appears to me" more difficult, than to ascertain by which of these

" processes it is really produced." * The same re-

* Dissertatio do Melhodo. In the sentence immediately foi-

lowing, Descartes mentions the general rule which he followed,

when such an embarrassment occurred. " Jlinc aliter me ex-


mark may (with a very few exceptions) be extend-

ed to every hypothetical theory which is unsupported

by any collateral probabilities arising from experience

or analogy ; and it sufficiently shews how infinitely

inferior such theories are, in point of evidence, to

the conclusions obtained by the art of the decypher-

er. The principles, indeed, on which this last art

proceeds, may be safely pronounced to be nearly in-

fallible.

In these strictures upon Hartley, I have endea-

voured to do as much justice as possible to his gene-

ral argument, by keeping entirely out of sight the

particular purpose which it was intended to serve.

By confining too much his attention to this, Dr

Reid has been led to carry, farther than was neces-

saryor reasonable, an indiscriminate zeal againstevery

speculation to which the epithet hypothetical can, in

any degree, be applied. He has been also led to

overlook the essential distinction between hypotheti-

cal inferences from one department of the Material

World to another, and hypothetical inferences from

the Material World to the Intellectual. It was

with the view of apologizing for inferences of the

latter description, that Hartley advanced the logical

principle which gave occasion to the foregoing dis-

cussion ; and, therefore, I apprehend, the proper

answer to his argument is this :—Granting your

" tricare non possum, quam si rursus aliqua experimenta quae.

" ram;quÊ talia sint, ut eorum idem non sit futurus eventus, si

" hoc modo quam si illo cxplicetur." The rule is excellent;

and it is only to be regretted, that so few exeraplificatioos of it

are to be found in his writings.

5


principle to be true in all its extent, it furnishes no

apology whatever for the Theory of Vibrations. If

the science of mind admit of any illustration from

the aid of hypotheses, it must be from such hypothe-

ses alone as are consonant to the analogy of its own

phenomena. To assume, as a fact, the existence of

analogies between these phenomena and those of

matter, is to sanction that very prejudice which it is

the great object of the inductive science of mind to

eradicate.

I have repeatedly had occasion, in some of my for-

mer publications, to observe, that the names of al-

most all our mental powers and operations are bor-

rowed from sensible images. Of this number are

intuition ; the discursive faculty ; attention ; reflec-

tion ; conception ; imagination ; apprehension ; com-

prehension ; abstraction ; invention ; capacity; pe-

netration ; acuteness. The case is precisely similar

with the following terms and phrases, relative to a

different class of mental phenomena ;—inclination;

aversion ; deliberation;pondering ; weighing the

motives of our actions;

yiefding to that motive

which is the strongest ;—expressions (it may be re-

marked in passing) which, when employed, with-

out a very careful analysis of their import, in the

discussion concerning the liberty of the will, gratui-

tously prejudge the very point in dispute ; and give

the semblance of demonstration, to what is, in fact,

only a series of identical propositions, or a sophistical

circle of words. *

* " Nothing," says Berkeley, " seems more to have contribut»

** ed towards engaging men in controversies and mistakes with

VOL. II. F f


That to the apprehensions of uneducated mensuch metaphorical or analogical expressions should

present the images and the things tijjjijied, insepar-

ably combined and blended together, is not wonder-

ful ; but it is the business of the philosopher to con-

quer these casual associations, and, by varying his

metaphors, when he cannot completely lay them

aside, to accustom himself to view the phenomena of

thought in that naked and undisguised state in

which they unveil themselves to the powers of con-

sciousness and reflection. To have recourse, there-

fore, to the analogies suggested by popular language,

fc.Y tiic purpose of eaylaining the operations of tlie

mind, instead of advancing knowledge, is to confirm

and to extend the influence of vulgar errors.

After having said so much in vindication of ana-

logical conjectures as steps towards physical discove-

ries, I thou^lit it right to caution my readers against

supposing, that what I have stated admits of any ap-

plication to analogical theories of the human mind.

Upon this head, however, I must not enlarge far-

ther at present. In treating of the inductive logic,

I have studiously confined my illustrations to those

branches of knowledge in which it has already been

exemplified with indisputable success j avoiding, for

obvious reasons, any reference to sciences in which

its utdity still remains to be ascertained

.

" reg<u'(i to the nature and (perations of tiic mind, than the being

" used to speak of ttiOHC things in terms borrowed from sensible

*' ideas. For example, the will is termed the motion of the soul.

*' This infuses a belief, that the mind of man is as a ball in mo-

" tion, impelled and determirvcd by the objects of sense, as ne-

*' cessarily as that is by the stroke of a racket,"

—

Principles of'

ûman Knowledge, $


III.

Supplemental Observations on the words Induction

awe? Analogy, as used in Mathematics.

Before dismissing the subjects of induction and

analogy, considered as methods of reasoning in Phy-

sics, it remains for me to take some sHght notice of

the use occasionally made of the same tenns in pure

Mathematics. Although, in consequence of the

very different natures of these sciences, the induc-

tion and analogy of the one cannot fail to differ wide-

ly from the induction and analogy of the other, yet,

from the general history of language, it may be safe-

ly presumed, that this application to both of a com-

mon phraseology, has been suggested by certain sup-

posed points of coincidence between the two cases

thus brought into immediate comparison. *

It has been hitherto, with a very few ifany excep-

tions, the universal doctrine of modern as well as of

ancient logicians, that ** no mathematical proposi-

** tion can be proved by induction.'* To this opi-

nion Dr Reid has given his sanction in the strongest

terms ; observing, that, " although in a thousand

" cases, it should be found by experience, that the

* I have already observed (see p. 367 of this volume), that

mathematicians frequently avail themselves of that sort of induc-

tion which Bacon describes " as proceeding by simple eiiumera-

" tion." The induction of which I am now to treat has very little

in common with the other, and bears a much closer resemblance

(to that recommended in the Novum Organon.

ELEMENTS OP THE PHILOSOPHY Chap. IV.

" area of a plane triangle is equal to the rectangle

*< under the base and half the altitude, this would" not prove that it must be so in all cases, and can-

" not be otherwise, which is what the mathematician

« affirms.'* *

That some limitation of this general assertion is

necessary, appears plainly from the well-known fact,

that induction is a species of evidence on which the

most scrupulous reasoners are accustomed, in their

mathematical inquiries, to rely with implicit confi-

dence ; and which, although it may not ofitselfAe-

monstrate that the theorems derived from it are ne-

cessarily true, is yet abundantly sufficient to satisfy

any reasonable mind that they hold universallij. It

was by induction (for example) that Newton disco-

vered the algebraical formula by which we are en-

abled to determine any power whatever, raised from

a binomial root, without performing the progressive

multiplications. The formula expresses a relation

between the exponents and the co-efficients of the

different terms, which is found to hold in all cases,

as far as the table of powers is carried by actual cal-

culation ;—from which Newton inferred, that if this

table were to be continued in injinitum, the same

Jbrmula would correspond equally with eveiy suc-

cessive power. There is no reason to suppose that

he ever attempted to prove the theorem in any other

way ; and yet there cannot be a doubt, that he was

as firmly satisfied of its being universally true, as if

he had examined all the different demonstrations of

* Pssays on the Intel). Powers, p. 6l5, 4to edit.

Sect. 4. Ot THE HUMAN MIND. 459

it which have since been given.* Numberless other

illustrations of the same thing might be borrowed,

both from arithmetic and geometry, t

* " The truth of this theorem was long known only by trial

** in particular cases, and by induction from analogy ; nor does it

*' appear that even Newton himself ever attempted any direct

" proof of it." (Hutton's Mnthcmatical Dictionary, Art. bino-

mial Theorem.) For some interesting information with re-

spect to the history of this discovery, see the very learned Intro-

duction prefixed by Dr Hutton to his edition of Sherwin's Ma-

thematical Tables; and the second volume (p. l65) of the Scrip-

tores Logaritkmici, edited by Mr Baron [viaseres.

+ In the Anthmetica Iiifinitorum of i>r Wallis, considerable

«se is made of the Method of Inductiun. *' A I'aide dCwe indue

" tion habilement menagee," sa^s Montucla, '• et du filde I'anam

•* logic dont il sgut toujours s'iiidtr avec succes, il soumit a la

*• geometrie une multitude d'objels qui lui avoient echappe jus-

«< qu' alors." (Hist, des Mathem. Tome II. p. 299-) '^^''s iiino-

vation in the established forms of mathematical reasoning gave

offence to some of his contemporaries ; in particular, to M. de

Fermat, one of the most distinguished geometers of the seventeenth

century. The ground of his objection, however (it is worthy of

notice), was not any douH of the conclusions obtained by Wallis

;

but because he thought that their truth might have been esta-

blished by a more legitimate and elegant process. " Sa faôii

** de demontrer, qui est fondee sur induction plutot que sur un

" raisonnement a la mode d'Archimede, fera quelque peine au.x

*' novices, qui veulent des syllogismes deinonstratifs depuis le

* commencement jusqu'a la fin. Ce n*est pas que je ne i*ap-

*' prouve, mais toutes ses propositions pouvant fetre demontrees

" vid ordinarid, legitimd, et Archimedced, en beaucoup moins de

*' paroles, que n'en contient son livre, je ne S9ai pas pourquoi il

** a prefere cette mani5re a I'ancienne, qui est plus convainquante

<' et plus elegante, ainsi que j'espere lui faire voir k nion premier

** loisir."—Lettre de M. de Fermat a M. le Chev. Kenelme

Bigby. (See Fermat's Varia Opera Mathematica, p. IplO For

454? ELEMENTS OF THE PHILOSOPHY Chap. IV.

Into what principles, it may be asked, is the va-

lidity of such a proof in mathematics ultimately re-

solvable ?—To me it appears to take for granted

certain general logical maxims ; and to imply a se-

cret process of legitimate and conclusive reasoning,

though not conducted agreeably to the rules of ma-

thematical demonstration, nor perhaps formally ex-

pressed in words. Thus, in the instance mentioned

by Dr Reid, I shall suppose, that I have first ascer-

tained experimentally the truth of the proposition

in the case of an equilateral triangle ; and that I

afterwards find it to hold in all the other kinds of

triangles, whether isosceles, or scalene, right-angled,

obtuse-angled, or acute-angled. It is impossible for

me not to perceive, that this property, having no

connection with any of the particular circumstances

which discriminate different triangles from each

other, must arise from something common to all tri-

angles, and must therefore be a universal property of

that figure. In like manner, in the binomial theo-

rem^ if the formula correspond with the table of

powers in a variety of particular instances (which

instances agree in no other respect, but in being

Wallis's reply to these strictures, see his Algebra^ Cap. Ixxix

;

and his Cotnmercium Epistolicutn.

In the Opuscules of M. Le Sage, I find the following sentence

quoted from a work of La Place, which I have not had an op-

portunity of seeing. The judgment of so great a master, on a

logical question relative to his own studies, is of peculiar value.

*' La methode d'induction, quoique excelknte pour dtconvrir des

" verites geveralesy ne doit pas dispenser de les demontrer avec

" rigueur."—Lepens donnces aux Ecoks Normaks, Prem. Vol. p,

380.


powers raised from the same binomial root), we must

conclude—and, I apprehend that our conclusion is

perfectly warranted by the soundest logic,—that it

is this common property which renders the theorem

true in all these cases, and consequently, that it miist

necessarily hold in eveiy other. Whether, on the

supposition that we had never had any previous ex-

perience of demonstrative evidence, we should have

been led, by the mere inductive process, to form the

idea of necessary truth, may perhaps be questioned;

but the slightest acquaintance with mathematics is

sufficient to produce the most complete conviction,

that whatever is U7iiversally true in that science,

must be true of necessity ; and, therefore, that a

universal, and a necessary truth, are, in the lan-

guage of mathematicians, synonymous expressions.

If this view of the matter be just, the evidence af-

forded by mathematical induction must be allowed

to differ radically from that of physical ; the latter

resolving ultimately into our instinctive expectation

of the laws of nature, and consequently, never

amounting to that demonstrative certainty, which

excludes the possibility of anomalous exceptions.

I have been led into this train of thinking by a

remark which La Place appears to me to have stated

in terms much too unqualified ;—" Que la marche

" de Newton, dans la decouverte de la gravitation

" universelle, a ete ei'actement la meme, que dans

" celle de la formule du binome." When it is re-

collected, that, in the one case, Newton's conclusion

related to a contingent, and in the other to a neces-

sary truth, it seems difficult to conceive how the

456 ELEIVIENTS OF THE PHILOSOPHY Chap. IV.

logical procedure which conducted him to both

should have been exactly the same. In one of his

queries, he has (in perfect conformity to the princi-

ples of Bacon's logic) admitted the possibility, that

" God may vary the laws of nature, and make worlds

" of several sorts, in several parts of the universe."

*' At least,*' he adds, '* 1 see nothing of contradic-

" tion in all this."* Would Newton have expressed

himself with equal scepticism concerning the univer-

sality of his binomial theorem ; or admitted the

possibility of a single exception to it, in the indefinite

progress of actual involution ? In sliort, did there

exist the slightest shade of difference between the

degree of his assent to this inductive result, and that

extorted from him by a demonstration of Euclid ?

Although, therefore, the mathematician, as well

as the natural philosopher, may, without any blame-

able latitude of expression, be said to reason by induc-

tion, when he draws an inference from the known

to the unknown, yet it seems indisputable, that, in

all such cases, he rests his conclusions on grounds

essentially distinct from those which form the basig

of experimental science.

The word analogy, too, as well as induction, is

common to physics, and to pure mathematics. It is

thus we speak of the analogy running through the

general properties of the different conic sections,

with no less propriety than of the analogy running

through the anatomical structure of different tribes

of animals. In some instances, these mathematical'

* Query 31.

Sect. 4. OF THE HUMAN MIND. 4^7

analogies are collected by a species of induction ; in

others, they arc inferred as consequences from more

general truths, in which they are included as parti-

cular cases. Thus, in the curves which have just

been mentioned, while we content ourselves (as

many elementary wi'iters have done) * with dedu-

cing their properties from mechanical descriptions

on a plane, we rise experimentally from a compari-

son of the propositions which have been separately

demonstrated with respect to each curve, to more

comprehensive theorems, applicable to all of them ;

whereas, when we begin with considering them in

their common origin, we have it in our power to

trace from the source, both their generic properties,

and their specific peculiarities. The satisfaction

arising from this last view of the subject can be con-

ceived by those alone who have experienced it ; al-

though I am somewhat doubtful whether it be not

felt in the greatest degree by such as, after having

risen from the contemplation of particular truths to

other truths more general, have been at last conduct-

ed to some commanding station, where the mutual

connections and affinities of the whole system are

brought, at once, under the range of the eye. Even,

however, before we have reached thisvantage-ground,

the contemplation of the analogy, considered mere-

ly as ^fact, is pleasing to the mind; partly from

the mysterious wonder it excites, and partly from

the convenient generalization of knowledge it af-=

fords. To the experienced mathematician this plea=

* L'Hospita', Sinison, Sac.


sure is farther enhanced, by the assurance which the

analogy conveys, of the existence of yet undiscover-

ed theorems, far more extensive and luminous than

those which have led him, by a process so indirect,

so tedious, and comparatively so unsatisfactoiy, to his

general conclusions.

In this last respect, the pleasure derived from ana-

logy in mathematics resolves into the same prin-

ciple with that which seems to have the chief share

in rendering the analogies among the different de-

partments of nature so interesting a subject of specu-

lation. In both cases, a powerful and agreeable sti-

mulus is applied to the curiosity, by the encourage-

ment given to the exercise of the inventive faculties,

and by the hope of future discovery, which is awaken-

ed and cherished. As the analogous properties (for

instance) of the conic sections, point to some gene-

ral theorems of which they are corollaries ; so the

analogy between the phenomena of Electricity and

those of Galvanism irresistibly suggests a confident,

though vague, anticipation of some general physical

law comprehending the phenomena of both, but dif-

ferently modified in its sensible results by a diversi-

ty of circumstances. * Indeed, it is by no means

impossible, that the pleasure we receive even from

those analogies which are the foundation of poetical

metaphor and simile, may be found resolvable, in

part, into the satisfaction connected with the sup-

posed discovery of truth, or the supposed acquisition

*>f knowledge ; the faculty of imagination giving to

* See Note (Y.)


these illusions a momentary ascendant over the sober

conclusions of experience ; and gratifying the un-

derstanding with a flattering consciousness of its

own force, or at least with a consolatory forgetful-

ness of its own weakness.

Section V.

Ofcertain 7nisapplkations of the words Ea:perience

and Induction in the phraseology of ModernScience.—Illustrationsfrom Medicine andfromPolitical Economy.

In the first Section of this Chapter, I endeavour-

ed to point out the characteristical peculiarities by

which the Inductive Philosophy of the Newtonians

is distinguished from the hypothetical systems of

their predecessors ; and which entitle us to indulge

hopes with respect to the permanent stability of their

doctrines, which might be regarded as chimerical,

if, in anticipating the future history of science, wewere to be guided merely by the analogy of its revo-

lutions in the ages that are past.

In order, however, to do complete justice to this

argument, as well as to prevent an undue extension

of the foregoing conclusions, it is necessary to guard

the x-eader against a vague application of the appro-

priate terms of inductive science to inquiries which

have not been rigorously conducted, according to the

rules of the inductive logic. From a want of atten-

tion to this consideration, there is a danger, on the

one hand, of lending to sophistry or to ignorance

the authority of those illustrious names whose steps


they profess to follow ; and, on the other, of bring-

ing discredit on that method of investigation, of

which the language and other technical arrange-

ments have been thus perverted.

Among the distinguishing features of the new^ lo-

gic, when considered in contrast with that of the

schoolmen, the most prominent is the regard which

it professes to pay to e^vjêrience^ as the only solid

foundation of human knowledge. It may be worth

while, therefore, to consider, how far the notion

commonly annexed to this word is definite and pre-

cise ; and whether there may not sometimes be a

possibility of its being employed in a sense more ge-

neral and loose, than the authors who are looked up

to as the great models of inductive investigation un-

derstood it to convey. *

* As the reflections which follow are entirely of a practical na-

ture, I shall express myself (as far as is cou'îstent with a due re-

gard to precision) agreeably to the modes of speaking in common

use ; without affecting a scrupulous attention to some speculative

distinctions, which, however curious and interesting, when con-

sidered in connection with the Theory of the Mind, do not lead

to any logical conclusions of essential importance in the conduct

of the Understanding. In such sciences, for example, as Astro-

nomy, Natural Philosophy, and Chemistry, which rest upon phe-

nomena open to the scrutiny of every inquirer, it would obvious-

ly be puerile in the extreme to attempt drawing the line between

facts which have been ascertained by our own personal observa-

tion, and those which we have implicitly adopted upon our faith

in the universal consent of the scientific world. The evidence, in

both cases, may be equally irresistible ; and sometimes the most

cautious reasoners may justly be disposed to consider that of tes-

timony as the least fallible of the two.

By far the greater part, indeed, of what is commonly called ex-


1

In the course of the abstract speculations contain-

ed in the preceding section, I have remarked, that

although the difference between the two sorts of evi-

dence, which are commonly referred to the separate

heads of experience and of analogy y be rather a dif-

' ference in degree than in kind^ yet that it is useful

peiimental knowlcilge, will be found, when traced to ils origin,

%o resolve entirely into our confidence in the judgment and the

veracity of our fellow-creatures ; nor (in the sciences already

mentioned) has this identification of the evidence of testimony

with that of experience, the slightest tendency to affect the legi«

timacy of our inductive conclusions.

In some other branches of knowledge (more particularly in

those political doctrines which assume as incontrovertible data

the details of ancient history), the authority of testimony is, for

obvious reasons, much more questionable ; and to dignify it, in

these, with the imposing character of experience, is to strengthen

one of the chief bulwarks of popular prejudices. This view of

the subject, however, although well entitled to the attention of the

logician, has no immediate connection with my present argu-

ment ; and accordingly, I shall make no scruple, in the sequel, to

comprehend, under the name of experience, the grounds of our as-

sent to all ih.p.facts on which our reasonings proceed, provided

only that the certainty of these facts be, on either supposition,

equally indisputable.

The logical errors which it is the aim of this section to correct,

turn upon a still more dangerous latitude in the use of this word

;

in consequence of which, the authority oi experience comes insen-

sibly to be extended to innumerable opinions resting solely on

supposed analogies ; while, not unfrequently, the language of Ba-

con is quoted in bar of any theoretical argument on the other side

of the question.

I have added this note, partly to obviate some criticisms, to

which my own phraseology may, at first sight, appear liable ; and

partly to point out the connection between the following discus«

sion, aod-some of the foregoing speculations.


to keep these terms in view, in order to mark the

contrast between cases which are separated from each

other by a very wide and palpable interval ;—more

especially, to mark the difference between an argu-

ment from individual to individual of the same spe-

cies, and an argument from species to species of the

same genus. As this distinction, however, when ac-

curately examined, turns out to be of a more vague

and popular nature than at first sight appears, it is

not surprising that instances should occasionally pre-

sent themselves, in which it is difficult to say, of the

evidence before us, to which of these descriptions it

ought to be referred. Nor does this doubt lead

merely to a question concerning phraseology : it

produces a hesitation which must have some effect

even on the judgment of a philosopher ; the maxims

to which we have been accustomed, in the course of

our early studies, leading us to magnify the evidence

of ej:perience as the sole test of truth ; and to de-

preciate that of analogy, as one of the most fertile

sources of error. As these maxims proceed on the

supposition, that the respective provinces of both are

very precisely defined, it is evident, that, admitting

them to be perfectly just in themselves, much dan-

ger may still be conceivable from their injudicious

application. I shall endeavour to illustrate this re-

mark by some familiar instances ; which, I trust,

will be sufficient to recommend it to the farther con-

sideration of future logicians. To treat of the sub-

ject with that minuteness of detail which is suited to

its importance, is incompatible with the subordinate

place which belongs to it in my general design.


It is observed by Dr Reid, * that, " in medicine,

" physicians must, for the most part, be directed in

" their prescriptions by analogy. The constitution

" of one human body is so like to that of another,

" that it is reasonable to think, that what is the

" cause of health or sickness to one, may have the

" same effect on another. And this," he adds, " is

** generally found true, though not without some

" exceptions.**

I am doubtful if this observation be justified by

the common use of language ; which, as far as I amable to judge, uniformly refers the evidence on which

a cautious physician proceeds, not to analogy, but to

ei'perience. The German monk, who (according to

the popular tradition), having observed the salutary

effects of antimony upon some of the lower animals,

ventured to prescribe the use of it to his own frater-

nity, might be justly said to reason analogically ;

—

inasmuch as his experience related to one species,

and his inference to another. But if, after having;

thus poisoned all the monks of his own convent, he

had persevered in recommending the same mineral

to the monks of another, the example of our most

correct writers would have authorized us to say (how

far justly is a different question), that he proceeded

in direct opposition to the evidence of ea:perience.

In offering this slight criticism on Dr Reid, I

would be very far from being understood to say, that

the common phraseology is more unexceptionable

than his. I would only remark, that his phraseo-

f Essays on the Intellect. Powers, p. 5o.

4f64f ELEMENTS OF THE PHILOSOPHY Chap. IV.

logy on this occasion is almost peculiar to himself;

and that the prevailing opinions, both of philoso-

phers and of the multitude, incline them to rank

the grounds of our reasoning in the medical art, at

a much higher point in the scale of evidence, than

what is marked by the word aiialogy. Indeed, I

should be glad to know, if there be any one branch

of human knowledge, in which men are, in general,

more disposed to boast of the lights of e^rperiaice,

than in the practice of medicine.

It would, perhaps, have been better for the world,

if the general habits of thinking and of speaking

had, in this instance, been more agreeable than they

seem to be in fact to Dr Reid's ideas ;—or, at least,

if some qualifying epithet had been invariably added

to the word ejcperience^ to shew with how very great

latitude it is to be understood, when applied to the

evidence on which the physician proceeds in the ex-

ercise of his art. The truth is, that, even on the

most favourable supposition, this evidence, so far as

it rests on experience, is weakened or destroyed by

the uncertain conditions of every new case to which

his former results are to be applied ; and that, with-

out a peculiar sagacity and discrimination in mark-

ing, not only the resembling, but the characteristi-

cal features of disorders, classed under the same

technical name, his practice cannot, with propriety,

be said to be guided by any one rational principle of

decision, but merely by blind and random conjec-

ture. The more successfully this sagacity and dis-

crimination are exercised, the more nearly does the

evidence of medical practice approach to that of ex»


perience ; but, in every instance, without exception,

so immense is the distance between them, as to ren-

der the meaning of the word ej^perience^ when ap-

plied to medicine, essentially different from its im-

port in those sciences where it is possible for us, in

all cases, by due attention to the circumstances of an

experiment, to predict its result with an almost in-

fallible certainty. *

Notwithstanding this very obvious consideration,

it has become fashionable among a certain class of

medical practitioners, since the lustre thrown on the

inductive logic of Bacon by the discoveries of New-

ton and the researches of Boyle, to number their art

with the other branches of experimental philosophy

;

* " L'art (ie conjecturoi cii Mcdecine nesauroit consister dans

" une suite de raisonnemens appuyes sur \\\\ vain systemc. C'est

" uniqueraent I'ait de comparer une inaladie qu'on doit guerir,

" avec les maladies semblables qu'on a <leja connues par son ex-

" perienceou parcelledes autres. Cetartconsiste memequelque-

" fois a appercevoir un rapport entre des maladies qui paro-

*' issent n'en point avoir, commc aussi dos differences essentielles,

" quoiqne fugitives, entre celles qui paroissent se ressembler le

" plus. Plus on aura rasseinble de fails, plus on sera en etat de

** conjecturer heureusement; suppose neanmoins qu'on ait d'ail-

" leurs cette justesse d'esprit que la nature seule peut donner.

" Ainsi le meilleur medecin u'est pas (comme le prejuge le sup-

•' pose) celui qui accumule en avcugle el en courant beaucoup de

" pratique, mais celui qui ne fait que des observations bien ap-

'• profondies, et qui joint a ces observations le nombre beaucoup

'' plus grand des observations faites dans tous les siecles par des

*' hommes animes du meme esprit que lui. Ces observations sent

" la veritable expericTwe du medecin."

—

D'Alembert, Edairdsse*

mens sur les Elemens de Pkilosophiey § vi.

VOL. II. <5 g


and to speak of the difference between the empiric

and the scientific physician, as if it were exactly

analogous to that between the cautious experimenter

and the hypothetical theorist in physics. Experi-

ence (we are told), and experience alone, must be

our guide in medicine, as in all tlie other depart-

ments of physical knowledge :—Nor is any innova-

tion, however rational, proposed in the established

routine of practice, but an accumulation of alleged

cases is immediately brought forward, as an experi-

mental proof of the dangers which it threatens.

It was a frequent and favourite remark of the late

Dr Cullen,—that there are more false facts current

in the world than false theories ; and a similar ob-

servation occurs, more than once, in the Novum Or-

ganon. *' Men of learning," says Bacon in one

passage, " are too often led, from indolence or cre-

" dulity, to avail themselves of mere rumours or

" whispers of e^vperioice, as confirmations, and

** sometimes as the very groundwork of their philo-

" sophy ; ascribing to them the same authority as if

" they rested on legitimate testimony. Like to a go-

" vernment which should regulate its measures, not

'* by the official information received from its own" accredited ambassadors, but by the gossipings of

" newsmongers in the streets. Such, in truth, is

" the manner in which the interests of philosophy,

" as far as experience is concerned, have been

" hitherto administered. Nothing is to be found

" which has been duly investigated ; nothing which

*' has been verified by a careful examination of

10


" proofs ; nothing which has been reduced to the

" standard of number, weight, or measure.'* *

This very important aphorism deserves the serious

attention of those who, while they are perpetually

declaiming against the uncertainty and fallacy of

systems, Ave themselves employed in amassing a

chaos of insulated particulars, w^hich they admit

upon the slenderest evidence. Such men, sensible

of their own incapacity for scientific investigation,

have often a malicious pleasure in destroying the fa-

brics of their predecessors j or, if they should be ac-

tuated by less unworthy motives, they may yet feel

a certain gratification to their vanity, in astonishing

the world with anomalous and unlooked-for pheno-

mena ;—a weakness which results not less naturally

from ignorance and folly, than a bias to premature

generalization irom the consciousness of genius.

—

Both of these weaknesses are undoubtedly adverse to

the progress of science ; but, in the actual state of

human knowledge, the former is perhaps the more

dangerous of the two.

In the practice of medicine (to which topic I wish

to confine myselfmore particularly at present), there

are a variety of other circumstances, which, abstract-

ing from any suspicion of bad faith in those on

whose testimony the credibility of facts depends,

have a tendency to vitiate the most candid accounts

of what is commonly dignified with the title of ea^pe-

rience. So deeply rooted in the constitution of the

mind is that disposition on which philosophy is graft-

* Nov. Org, Lib. I. Aph. xcviji.

46*8 ELEMENTS OF THE PHILOSOPHY Ciiap. IV.

etl, that the simplest narrative of the most illiterate

observer involves more or less of hypothesis ; nay,

in general, it will be found, that, in proportion to

his ignorance, the greater is the number of conjec-

tural principles involved in his statements.

A village-apothecary (and, if possible, in a still

greater degree, an experienced nurse) is seldom able

to describe the plainest case, without employing a

phraseology ofwhich every word is a theory ; where-

as a simple and genuine specification of the pheno-

mena which mark a particular disease ;—a specifi-

cation unsophisticated by fancy, or by preconceived

opinions, may be regarded as unequivocal evidence

of a mind trained by long and successful study to

the most difficult of all arts, that of the faithful in-

terpretation ofnature.

Independently, however, of all these circum-

stances, which tend so powerfully to vitiate the data

whence the physician has to reason ; and supposing

his assumed facts to be stated, not only with the

most scrupulous regard to truth, but with the most

jealous exclusion of theoretical expressions, still the

evidence upon which he proceeds is, at best, conjec-

tural and dubious, when compared with what is re-

quired in chemistry or in mechanics. It is seldom,

if ever, possible, that the description of any medical

case can include all the circumstances with which

the result wâs connected ; and, therefore, how true

soever the facts described may be, yet when the con-

clusion to which they lead comes to be applied as a

general rule in practice, it is not only a rule rashly

drawn from one single experiment, but a rule trans-


ferred from a case imperfectly known, to another of

which we are equally ignorant. Here, too, it will

be found, that the evidence of experience is incom-

parably less in favour of the empiric, than ofthe cau-

tious theorist ; or rather, .that it is by cautious theo-

ry alone, that experience can be rendered of any va-

lue. Nothing, indeed, can be more absurd than to

contrast, as is commonly done, experience with

theory, as if they stood in opposition to each othei'.

Without tlieory (or, in other words, without gene-

ral principles, inferred from a sagacious comparison

of a variety of phenomena), experience is a blind

and useless guide ; while, on the other hand, a legi-

timate theory (and the same observation may be ex-

tended to hypothetical theories, supported by nume-

rous analogies) necessarily presupposes a knowledge

of coniiected and well-ascertained facts, more com-

prehensive by far than any mere empiric is likely to

possess. When a scientific practitioner, according-

ly, quits the empirical routine of his profession, in

quest of a higher and more commanding ground, he

does not proceed on the supposition, that it is pos-

sible to supersede the necessity ofexperience by the

most accurate reasonings a 'priori ; but, distrusting

conclusions which rest on the observation of this or

that individual, he is anxious, by combining those

of an immense multitude, to separate accidental con-

junctions from established connections, and to ascer-

tain those laws of the human frame which rest on '

the universal experience of mankind. The idea of

following nature in the treatment of diseases ;—an

idea which, I believe, prevails more and more in the


practice of every physician, in proportion as his'

views are enlarged by science, is founded, not on

hypothesis, but on one of the most general laws yet

known with respect to the animal economy ; and it

implies an acknowledgment, not only of the vanity

of abstract theories, but of the limited province of

human art.*

These slight remarks are sufficient to shew how

vague and indeterminate the notion is, which is

commonly annexed to the word e.vperience by the

most zealous advocates for its paramount authority

in medicine. They seem further to shew, that the

question between them and their adversaries amounts

to little more than a dispute about the comparative

advantages of an experience guided by penetration

and judgment, or of an experience which is to su-

persede all exercise of our rational faculties ; of an

experience accurate, various, and discriminating, or

of one which is gross and undistinguishing, like the

perceptions of the lower animals.

* " Gaudet corpus vi prorsus mirabili, qua contra morbos se

" tueatiir ; multos arceat ; multos jam inchoates quam optinie et

" citissime solvat ; aliosque sue mode, ad felicem exilum len-

" tius perducat.

" Usee, Autocrateia, vis Natures medicatrixf vocatur ; me-

" dicis, philosophis, notissima, et jure celeberrima. Haec sola

" ad multos morbos sanandos sufficit, in omnibus fere prodest:

" Quin et medicamenta sua natura optima, tanturn solummodo

** prosuut, quantum hujus vires insitas excilent, dirigant, guber-

" nent. Medicina cnim neque agit in cadaver, neque repug-

" nante natura aliquid proficit."

Conspectus Medicinae Theoreticae. Auctore Jacobo Gregory,

M. D. §§ 6% 60. (Edin. 1782.)


Another department of" knowledge in which con-

stant appeals are made to ea:perie7ice, is the science

o^politics ; and, in this science also, I apprehend,

as well as in the former, that word is used with a far

greater degree of latitude than is generally suspect-

ed. Indeed, most of the remarks which have been

already offered on the one subject may be extended

(mutatis mutandis) to the other. I shall confine

my attention, therefore, in what follows, to one or

two peculiarities by which politics is specifically and

exclusively characterized as an object of study ; and

which seem to remove the species of evidence it ad-

mits of, to a still greater distance than that of medi-

cine itself, from what the word experience naturally

suggests to a careless inquirer.

The science of politics may be divided into two

parts ; the first having for its object the theory of

government ; the second, the general principles of

legislation. That I may not lose myself in too wide

a field, I shall, on the present occasion, wave all

consideration of the former ; and, for the sake of

still greater precision, shall restrict my remarks to

those branches of the latter, which are compre-

hended under the general title of Political Eca-

nomy ;—a phrase, however, which I wish to be

here understood in its most extensive meaning. *

They who have turned their attention, during

the last century, to inquiries connected with popu-

lation, national wealth, and other collateral subjects,

may be divided into two classes ; to the one of

* See Note (Z.)


which we may, for the sake of distinction, give the

title 0^ political arit/wieticians^ or statistical collec-

tors ; to the other, that of political economists^ or

political philosophers. The former, are generally

supposed to have the evidence of t'^;pme;zc6' in their

favour, and seldom fail to arrogate to themselves ex-

clusively the merit of treading closely in the foot-

steps of Bacon. In comparison v\'ith themy the lat-

ter are considered as little better than visionaries,

or, at least, as entitled to no credit whatever, when

their conclusions are at variance with the details of

statistics.

In opposition to this prevailing prejudice, it may,

with confidence, be asserted, that, in so far as either

of these branches of knowledge has any real value,

it must rest on a basis of v»ell-ascertained facts ; and

that the difference between them consists only in the

different nature of the facts with which they are re-

spectively conversant. The facts accumulated by

the statistical collector are merelyparticular results

,

which other men have seldom an opportunity of ve-

rifying or of disproving ; and which, to those who

consider them in an insulated state, can never af-

ford any important information. The facts which

the political philosopher professes to investigate are

exposed to the examination of all mankind ; and

while they enable him, like the general laws of phy-

sics, to ascertain numberless particulars by synthetic

reasonings they furnish the means of estimating the

credibility of evidence resting on the testimony of

individual observers.

It is acknowledged by Mr Smith, whh respect to


himself, that he had " no great faith in political

*' arithmetic ;" * and I agree with him so far as to

think, that little, if any, regard is due to 2i particular

phenomenon, when stated as an objection to a con-

clusion resting on the general laws which regulate

the course of human affairs. Even admitting the

phenomenon in question to have been accurately ob-

served, and faitlifully described, it is yet possible

that we may be imperfectly acquainted with that

combination of circumstances whereby the effect is

modified ; and that, if these circumstances were

fully before us, this apparent exception would turn

out an additional illustration of the very truth which

it was brought to invalidate.

If these observations be just, instead of appealing

to political arithmetic as a check on the conclusions,

of political economy, it would often be more reason,

able to have recourse to political economy as a check

on the extravagancies of political arithmetic. Nor

will this assertion appear paradoxical to those who

consider, that the object of the political arithmeti-

cian is too frequently to record apparent exceptions

to rules sanctioned by the general experience ofman-

kind ; and, consequently, that in cases where there

is an obvious or a demonstrative incompatibility be-

tween the alleged exception and the general prin-

ciple, the fair logical inference is not against the

truth of the latter, but against the possibility of the

former.

It has long been an established opinion among the

* Weiilih. of Nations, Vol. 11. pw 310, .Qth edit. •

4>74f ELEMENTS OP THE PHILOSOPHY Cliap. IV.

most judicious and enlightened philosophers,—that,

as the desire of bettering our condition appears

equalhffrom a carefid review of the motives rvhich

habitually influence our own conduct^ and from a

general survey of the history of our species, to be

the masterspring of human industry, the labour of

slaves never can be so productive as that of free-

men. Not many years have elapsed, since it was

customary to stigmatize this reasoning as visionary

and metaphysical ; and to oppose to it that species

of evidence to which we were often reminded that

all theories must bend ;—the evidence of experi-

mental calculations, furnished by intelligent and cre-

dible observers on the other side of the Atlantic.

An accurate examination of the fact has shewn how

wide of the truth these calculations were ;—^but, in-

dependently of any such detection of their fallacy,

might it not have been justly affirmed, that the ar-

gument from eo'perience was decidedly against their

credibility ;—the facts appealed to resting solely

upon the good sense and good faith of individual

witnesses ; while the opposite argument, drawn

from the principles of the human frame, was sup-

ported by the united voice of all nations and ages ?

If we examine the leading principles which run

through Mr Smith's Inquiry into the Nature and

Causes of the Wealth of Nations, we shall find, that

all of them are generaifacts or general results, analo-

gous to that which has been just mentioned. Of this

kind, for instance, are the following propositions,

—

from which a very large proportion of his charac-

teristical doctrines follow, as necessary and almost

Sect 5. OP THE HUMAN MIND. 475

manifest corollaries : That what we call the Politi-

cal Order, is much less the effect of human contri-

vance than is commonly imagined :—That every

man is a better judge of his own interest than any

legislator can be for him ; and that this regard to

private interest (or, in other words, this desire

of bettering our condition) may be safely trusted

to as a principle of action universal among menin its operation ;— a principle stronger, indeed,

in some than in others, but constant in its ha-

bitual influence upon all :—That, where the rights

of individuals are completely protected by the ma-

gistrate, there is a strong tendency in human af-

fairs, arising from what we are apt to consider

as the selfish passions of our nature, to a pro-

gressive and rapid improvement in the state of

society :—That this tendency to improvement in

human affairs is often so very powerful, as to cor-

rect the inconveniencies threatened by the errors

of the statesman :—And that, therefore, the reason-

able presumption is in favour of every measure

which is calculated to afford to its farther develope-

ment, a scope still freer than what it at present en-

joys ; or, which amounts very nearly to the same

thing, in favour of as great a liberty in the employ-

ment of industry, of capital, and of talents, as is

consistent with the security of property, and of the

other rights of our fellow-citizens.—The premises,

it is perfectly obvious, from which these conclusions

are deduced, are neither hypothetical assumptions,

nor metaphysical abstractions. They are practical

maxims of good sense, approved by the experience


of men in all ages of the world ; and of which, if

we wish for any additional confirmations, we have

only to retire within our own bosoms, or to open

our eyes on what is passing around us.

From these considerations it would appear, that

in politics, as well as in many of the other sciences,

the loudest advocates for experience are the^least en-

titled to appeal to its authority in favour of their

dogmas; and that the charge of a presumptuous

confidence in human wisdom and foresight, which

they are perpetually urging against political philo-

sophers, may, with far greater justice, be retorted

on themselves. An additional illustration of this

is presented by the strikingly contrasted effects of

statistical and of jihilosophical studies on the intel-

lectual habits in general ;—the former invariably

encouraging a predilection for restraints and checks,

and all the other technical combinations of an anti-

quated and scholastic policy ;—the latter, by in-

spiring, on the one hand, a distrust of the human

powers, when they attempt to embrace in detail, in-

terests at once so complicated and so momentous ;

and, on the other, a religious attention to the de-

signs of Nature, as displayed in the general laws

which regulate her economy ;—leading, no less ir-

resistibly, to a gradual and progressive simplifica-

tion of the political mechanism. It is, indeed, the

never failing result of all sound philosophy, to hum-

ble, more and more, the pride of science before that

Wisdom which is infinite and divine ;—whereas, the

farther back we carry our researches into those ages,

tlie institutions of which have been credulously re-


garded as monuments of the superiority of unsophis-

ticated good sense, over the false refinements of

modern arrogance, we are the more struck with the

numberless insults offered to the most obvious sug-

gestions of nature and of reason. We may remark

this, not only in the moral depravity of rude tribes,

but in the universal disposition which they discover

to disfigure and distort the bodies of their infants j

—

in one case, new-modelling the form of the eyelids

;

—in a second, lengthening the ears ;—in a third,

checking the growth of the feet ;—in a fourth, by

mechanical pressures applied to the head, attacking

the seat of thought and intelligence. To allow the

human form to attain, in perfection, its fair propor-

tions, is one of the latest improvements of civilized

society ; and the case is perfectly analogous in those

sciences which have for their object to assist nature

in the cure of diseases ; in the developement and

improvement of the intellectual faculties ; in the

correction of bad morals j and in the regulations of

political economy.


Section VI.

X)fthe Specidat'ion conceiving Final Causes.

I.

Opinion of Lord Bacon on the subject.—Final

Causes rejected hi) Descartes, and by the majo-

rity of French Philosophers,—Recognised as

legitimate Objects of research by Newton^—T'aciily ackno'wledged by all as a useful logical

Guide, even m Sciences which have no immediate

relation to Theology.

The study of Final Causes may be considered in

two different points of view ; first, as subservient to

the evidences of natural religion ; and, secondly, as

a guide and auxiliary in the investigation of physi-

cal laws. Of these view^s it is the latter alone which

is immediately connected with the principles of the

inductive logic ; and it is to this, accordingly, that I

shall chiefly direct my attention in the following

observations. I shall not, however, adhere so scru-

pulously to a strict arrangement, as to avoid all re-

ference to the former, where the train of my reflec-

tions may naturally lead to it. The truth is, that

the two speculations will, on examination, be found

much more nearly allied, than might at first sight be

apprehended.

I before observed, that the phrase Final Cause

was first introduced by Aristotle ; and that the ex-

tension thus given to the notion of causation contri-

buted powerfully to divert the inquiries of his fol-


lowers from the proper objects of physical science.

Ill reading the strictures of Bacon on this mode of

philosophizing, it is necessary always to bear in mind

that they have a particular reference to the theories

of the schoolmen ; and, if they should sometimes

appear to be expressed in terms too unqualified, due

allowances ought to be made for the undistinguish-

ing zeal of a reformer, in attacking prejudices

consecrated by long and undisturbed prescription.

*' Causarum Jinalium inqidsitio steriUs esty et tan-

" qiiam Virgo Deo consecrata^ nihil parit.^* Hada similar remark occurred in any philosophical work

of the eighteenth century, it might, perhaps, have

been fairly suspected to savour of the school of Epi-

curus ; although, even in such a case, the quaint-

ness and levity of the conceit would probably have

inclined a cautious and candid reader to interpret

the author's meaning with an indulgent latitude.

On the present occasion, however. Bacon is his

own best commentator ; and I shall therefore quote,

in a faithful, though abridged translation, the pre-

paratory passage by which this allusion is intro-

duced.

" The second part of metaphysics is the investi-

" gation oijinal causes ; which I object to, not as a

" speculation which ought to be neglected, but as

" one which has, in general, been very improperly

" regarded as a branch of physics. If this were

" merely a fault of arrangement, I should not be

" disposed to lay great stress upon it ; for arrange-

" ment is useful chiefly as a help to perspicuity, and**^ does not affect the substantial matter of science :


** But, in this instance, a disregard of 7nethodhas oc-

** casioned the most fatal consequences to philosopliyj

*' inasmuch as the consideration of Ji?ial causes in

" physics has supplanted and banished the study of

*' physical causes ; the fancy amusing itself with il-

" lusory explanations derived from the fonner, and" misleading the curiosity from a steady prosecution

" of the latter.'* After illustrating this remark by

various examples, Bacon adds :*' I would not, how-

*' ever, be understood, by these observations, to in-

*' sinuate, that the final causes just mentioned may" not be founded in truth, and, in a metaphysical

" view, extremely worthy of attention ; but only,

" thatwhen such disquisitions invade and overrun the

" appropriate province of phi/sicSy they are likely to

*' lay waste and ruin that department of knowledge."

The passage concludes with these words : " And so

" much concerning metaphysics ; the part of which

" relating to ^nal causes^ I do not deny, has been

*' often enlarged upon in physical, as well as in me-*' taphysical treatises. But while, in the latter of

" these, it is treated of with propriety, in the for-

*' mer, it is altogether misplaced ; and that, not

*' merely because it violates the rules of a logical or-

** der, but because it operates as a powerful obstacle

** to the progress of inductive science." *

The epigrammatic maxim which gave occasion to

these extracts has, I believe, been oftener quoted

(particularly by French writers) than any other sen-

tence in Bacon's works ; 'and, as it has in general

* Dc Augin. Scicnt. Lib. JII. Cap, iv. v. See Note (AA.)


been stated, without any reference to the context,

in the fonn of a detached aphorism, it has been

commonly supposed to convey a meaning widely dif-

ferent from what appears to have been annexed to it

by the author. The remarks with which he has pre-

faced it, and which I have here submitted to the

consideration of my readers, sufficiently shew, not

only that he meant his proposition to be restricted

to the abuse of final causes in the physics of Aristo-

tle, but that he was anxious to guard against the

possibility of any misapprehension or misrepresenta-

tion of his opinion. A farther proof of this is af-

forded by the censure which, in the same paragraph,

he bestows on Aristotle, for '* substituting Nature,

" instead of God, as the fountain of final causes

;

" and for treating of them rather as subservient to

" logic than to theology."

A similar observation may be made on another

sentence in Bacon, in the interpretation of which a

very learned writer, Dr Cudworth, seems to have al-

together lost sight of his usual candour. " Incredi-

*' bile est quantum agmen idolorum philosophise im-

" miserit, naturalium operationum ad similitudinem

" actionum humanarum reductio." " If,'* says

Cudworth, " the Advancer of Learning here speaks

*' of those who unskilfully attribute their own pro-

" perties to inanimate bodies (as when they say, that

" matter desires forms as the female does the male,

*' and that heavy bodies descend down bi/ appetite

" towards the centre, that they may rest therein),

" there is nothing to be reprehended in the passage.

VOL. II. H h


« But, if his meaning be extended further to take

" away all final causes from the things of nature,

" then is it the very spirit of atheism and infidelity.

" It is no idol of the cave or den (to use that af-

" fected language), that is, no prejudice or fallacy

" imposed on ourselves, from the attributing our

** own animalish properties to things without us, to

" think that the frame and system of this whole

" world was contrived by a perfect understanding

" and mind."

It is difficult to conceive that any person who had

read Bacon's works, and who, at the same time, was

acquainted with the theories which it was their great

object to explode, could, for a moment, have hesitat-

ed about rejecting the latter interpretation as alto-

gether absurd ; and yet the splenetic tone which

marks the conclusion of Cudworth's strictures, plain-

ly shews that he had a decided leaning to it, in pre-

ference to the former. * The comment does no

* Even \\\Gformer interpretation is not agreeable (as appears

manifestly from the context) to Bacon's idea. The prejudices

which he has here more particularly in view, are those which

take their rise from a bias in the mind to imagine a greater

equality and uniformity in nature than really exists. As an in-

stance of this, he mentions the universal assumption among the

ancient astronomers, that all the celestial motions are performed

in orbits perfectly circular ;—an assumption which, a few years

before Bacon wrote, had been completely disproved by Kepler.

To this he adds some other examples from physics and chemis-

try ; after which he introduces the general reflection animadvert-

ed on by Cudworth.—The whole passage concludes with these

words : " Tanta est harmoniai discrepantia inter spiritum homi-

" nis et spiritum raundi."

Sect. 6. OFJHE HUMAN MINt). 483

honour to his liberality ; and, on the most favourable

supposition, must be imputed to a superstitious re-

verence for the remains of Grecian wisdom, accom-

panied with a corresponding dread of the unknown

dangers to be apprehended from philosophical inno-

vations. Little was he aware, that, in turning the

attention of men from the history of opinions and

systems to the observation and study of nature, Ba-

con was laying the foundation ot a bulwark against

atheism, more stable and impregnable than the unit-

ed labours of the ancients were able to rear ;—â

bulwark which derives additional strength from

every new accession to the stock of human know-

ledge. *

The criticism may appear minute ; but I cannot forbear to

mention, as a proof of the carelessness with which Cudworth had

read Bacon, that the prejudice supposed by the former to be-

long to the class of idula specus, is expressly quoted by the latter,

as an example of the idulu tribus.—See the 5th Book De Aug-

ment, Scient. Chap, iv.'

* " Extabit eximium Newtoni opus adversus Atheorum impe-

" tus munitissimum presidium."

—

Cotesii Prof, in Edit. Secund,

Princip.

In the above vindication of Bacon, I have abstained from any

appeal to the instances in which he has himself forcibly and elo-

quently expressed the same sentime.its here ascribed to him ; be-

cause I conceive that an author's real opinions are to be most in-

disputably judged of from the general spirit and tendency of his

writings. The following passage, however, is too precious a do-

cument to be omitted on the present occasion. It is, indeed,

one of the most hackneyed quotations in our language; but it

forms, on that very account, the more striking a contrast to the

voluminous and now neglected erudition displayed by Cudworth

in defence of the same argument.

" I had rather believe all the fables in the I.ei;end, and the

484 ELEMENTS OF THE PHILOSOPHY Chap. IV •

Whether Bacon*s contempt for the Final Causes

of the Aristotelians has not carried him to an ex-

treme in recommending the total exclusion of them

from physics, is a very different question ; and a

question of much importance in the theory of the in-

ductive logic. My own opinion is, that his views

on this point, if considered as applicable to the pre-

sent state of experimental science, are extremely li-

mited and erroneous. Perhaps, at the time when

he wrote, such an exclusion may have appeared ne-

cessary, as the only effectual antidote against the er-

rors which then infected every branch of philoso-

phy ; but granting this to be true, no good reason

can be given for continuing the same language, at a

period when the proper object of physics is too well

understood, to render it possible for the investigation

of final causes to lead astray the most fanciful

theorist. What harm can be apprehended from

" Talmud, ami the Alcoran, than that this universal frame is

" without a mind! It is true that a little philosophy inclineth

" man's mind to atheism ; but depth in philosophy bringeth

" men's minds about to religion ; for while the mind of man look-

" eth upon second causes scattered, it may sometimes rest in

*' them, and go no farther; but when it beholdeth the chain of

" them confederate and linked together, it must needs fly to Pro-

** vidence and Deity : nay, even that school which is most ac-

" cused of alheism, doth most demonstrate religion ; that is, the

" school of Iêucippus, and Democritus, and Epicurus ; for it is

" a thousand times more credible, that four mutable elements

" and one immutable fifth essence, duly and eternally placed,

" need no God, than that an army of infinite small portions, or

" seeds unplaced, should have produced this order and beauty

" without a divine marshal."

—

Bacons Essays,

1

S^Ct. 6. OF THE HUMAN MIND. 485

remai'king those proofs of design vvliicli fall under

the view of the physical inquirer in the course of

his studies ? Or, if it should be thouglit foreign to

his province to speak of design, he may, at least, be

permitted to remark what ends are really accom-

plished by particular means ; and what advantages

result from the general laws by which the pheno-

mena^ of nature are regulated. In doing this, he

only states a fact ; and if it be illogical to go far-

ther, he may leave the inference to the moralist or

the divine.

In consequence, however, of the vague and com-

mon-place declamation against final causes, sanction-

ed (as has been absurdly supposed) by those detached

expressions of Bacon, which have suggested the fore-

going reflections, it has, for many years past, be-

come fashionable to omit the consideration of them

entirely, as inconsistent with the acknowledged rules

of sound philosophizing ;—a caution (it may be re-

marked by the way) which is most scrupulously ob-

served by those writers who are the most forward to

censure every apparent anomaly or disorder in the

economy of the universe. The effect of this has

been, to divest the study of nature of its most at-

tractive charms j and to sacrifice to a false idea of

logical rigour, all the moral impressions and plea-

sures which physical knowledge is fitted to yield. *

* " If a traveller," says the great IMr Boyle, " being in some" ill-inhabited eastern country, should come to a large and fair

<' building, such as one of the most stately of those they call ca-

** ravanzeras, though he would esteem and be delighted with the

" magnificence of the structure, and the commodiousness of the


Nor is it merely in a moral view that the con-

sideration of uses is interesting. There are some

parts of nature in which it is necessary to complete

the physical theory ; nay, there are instances, in

which it has proved a powerful, and perhaps indis-

pensable, organ of j'->//^5ic^// discovery. That Bacon

should not have been aware of this, will not appear

surprising, when it is recollected, that the chief facts

which justify the observation have been brought to

light since his time.

Of thesej^cÂ^, the most remarkable are furnished

by the science of anatomy. To understand the

structure of an animal body, it is necessary not only

to examine the co?ifb?"matio?i of the parts, but to

consider theirfunctions ; or, in other words, to con-

sider their ends and uses : Nor, indeed, does the

most accurate knowledge of the former, till per-

fected by the discovery of the latter, afford satisfac-

tion to an inquisitive and scientific mind. Every

anatomist, accordingly, whatever his metaphysical

creed may be, proceeds, in his researches, upon the

maxim, that no organ exists without its appropriate

destination ; and although he may often fail in his

*' apartments, yet supposing it to have been erected but for the

*' honour or the pleasure of the founder, he would commend so

" stately a fabric, without thanking him for it ; but, if he were

" satisfied that this commodious building was designed by the

" founder as a receptacle for passengers, who were freely to have

*' the use of the many conveniences the apartments afforded, he

" would then think himself obliged, not only to praise the magni-

*' ficence, but with gratitude to acknowledge the bounty and the

" philanthropy of so munificent a benefactor."—iJoj^/c'* WorkSy

Vol \\. p. 517. Folio edition.


attempts to ascertain what this destination is, he

never carries his scepticism so far, as, for a moment,

to doubt of the general principle. I am inclined to

think, that it is in this way the most important steps

in physiology have been gained ; the curiosity being

constantly kept alive by some new problem in the

animal machine j and, at the same time, checked in

its wanderings, by an irresistible conviction, that no-

thing is made in vain. The memorable account

given by Mr Boyle of the circumstances which led

to the discoveiy of the circulation of the blood, is

but one of the many testimonies which might be

quoted in confirmation of this opinion.

" I remember, that when I asked our famous

" Harvey, in the only discourse I had with him" (which was but a little while before he died), what

" were the things which induced him to think of a

" circulation of the blood ? he answered me, that

" when he took notice, that the valves in the veins

" of so many parts of the body were so placed, that

" they gave free passage to the blood towards the

" heart, but opposed the passage of the venal blood

" the contrary way, he was invited to think, that so

** provident a cause as nature had not placed so

" many valves without design ; and no design seem-

" ed more probable, than that, since tlie blood could

" not well, because of the interposing valves, be sent

*• by the veins to the limbs, it should be sent

" through the arteries, and return through the veins,

** whose valves did not oppose its course that way."*

* IJoyle's Works, Vol. IV. p. 539- Folio ed. See Outlines

of Moral Philosophy, p. 185. (Kdin. 1793.)

488 ELEMENTS OF THE PHILOSOPHY Chap. I\'.

This perception of design and contrivance is more

peculiarly impressive, when we contemplate those

instances in the animal economy, in which the same

effect is produced, in different combinations of cir-

cumstances, by different means ;—when we compare,

for example, the circulation of the blood in the foe-

tus, with that in the body of the animal after it is

born. On such an occasion, how is it possible to

withhold the assent from the ingenious reflection of

Baxter !** Art and means are designedly multi-

" plied, that we might not take it for the effects of

" chance ; and, in some cases, the method itself is

" different, that we might see it is not the effect of

" surd necessity." *

The reasoning here ascribed to Harvey seems now so very na-

tural and obvious, that some have been disposed to question his

claim to the high rank commonly assis^ned to him among the im-

provers of science. The late Dr William Hunter has said, that

after the discovery of the valves in the veins, which Harvey

learned, while in Italy, from his master Fabricius ab Aquapen-

dente, the remaining step might easily have been made by any

person of common abilities. " This discovery," he observes,

" set Harvey to work upon the use of the heart and vascular sys-

" tem in animals ; and, in the course of some years, he was so

" happy as to discover, and to prove beyond all possibility of

" doubt, the circulation of the blood." He afterwards expresses

his astonishment that this discovery should have been left for

Harvey ; adding, that " Providence meant to reserve it for /«'»?,

" and would not let men see "what teas before them, nor understand

" "what they read."—Hunter s Introdvctory Lectures, p. 42, et seq.

Whatever opinion be formed on this point, Dr Hunter's re-

marks are valuable, as an additional proof of the regard paid by

anatomists to Final Causes, in the study of physiology.

See also Haller, Elem. Physiolog. Tom. I. p. 204.

.* Inquiry into the Nature oftheHuman Soul, Vol I. p. 135.

(3d edit.)


The study of comparative anatomy leads, at every

step, so directly and so manifestly to the same con-

clusion, that even those physiologists who had no-

thing in view but the advancement of their own

The following passage from an old English divine may be of

iise for the farther illustration of this argument. I quote it with

the greater confidence, as I find that the most eminent and origi-

nal physiologist of the present age (M. Cuvier) has been led, by

his enlightened researches concerning the laws of the animal

economy, into a train of thinking strikingly similar.

" Man is always mending and altering his works ; but nature

** observes the same tenor, because her works are so perfect, that

" there is no place for amendments, nothing that can be repre-

" hended. The most sagacious men in so many ages have not

** been able to find any flaw in these divinely contrived and form-

" ed machines ; no blot or error in this great volume of the

" world, as if anything had been an imperfect essay at the first;

" nothing that can be altered for the better ; nothing but if it

" were altered would be marred. Ttiis could not have been, had

" man's body been the work of chance, and not counsel and pro-

" vidence. Why sliouhl there be constantly the same parts ?

" Why should they retain constantly the same places ? Nothing

" so contrary as constancy and chance. Should I see a man" throw the same number a thousand times together upon but

" three dice, could you persuade me that this were accidental,

" and that there was no necessary cause for it ? How much more

*' incredible then is it, that constancy in such a variety, such a

" multiplicity of parts, should be the result of chance ? Neither

" yet can these works be the effects of Necessity or Fate, for then

" there would be the same constancy observed in the smaller as

" well as in the larger parts and vessels ; whereas, there we see

" nature doth, as it were, sport itself, the minute ramifications

" of all the vessels, veins, arteries, and nerves, infinitely varying

" in individuals of the same species, so that 'they are not in any

^' two alike."

—

Ray^s Wisdom of God in the Creation.


science, unanimously agree in recommending the

dissection of animals of different kinds, as the most

effectual of all helps for ascertaining theJiinctions of

the various organs in the human frame ;—tacitly as-

suming, as an incontrovertible truth, that, in propor-

tion to the variety of means by which the same effect

is accomplished, the presumption increases, that this

effect was an e?id in the contemplation of the artist.

" The intention of nature," says one author, " in

" the formation of the different parts, can nowhere

" be so well learned as from comparative anatomy ;

" that is, if we would understand physiology, and

" reason on the functions of the animal economy,

*' Nature,'* says Cuvier, " while confining herself strictly with-

" in those limits which the conditions necessary for existence

" prescribed to her, has yielded to her spontaneous fecundity

" wherever these conditions did not limit her operations ; and

" without ever passing beyond the small number of combinations,

" that can be realized in the essential modifications of the im-

" portant organs, she seems to have given full scope to her fancy,

" in filling up the subordinate parts. With respect to these, it is

" not inquired, whether an individual form, whether a particular

" arrangement, be necessary ; it seems often not to have been

" asked, whether it be even useful, in order to reduce it to prac-

" tice ; it is sufficient that it be possible, that it destroy not the

'* harmony of the whole; Accordingly, as we recede from the

" principal organs, and approach to those of less importance, the

" varieties in structure and appearance become more numerous

;

" and when we arrive at the surface of the body, where the parts

" the least essentia), and whose injuries arc the least momentous,

" are necessarily placed, the number of varieties is so great, that

" the conjoined labours _of naturalists have not yet been able to

" give us an adequate idea of them."

—

Legons d'Anatomic Corn-

pane.


** we must see how the same end is brought about

" in other species.—We must contemplate the part

" or organ in different animals ; its shape, position,

•* and connexion with the other parts ; and obseiTe

** what thence arises. If we find one common" EFFECT constantly produced, though in a very

*' different way, we may safely conclude that this is

" the use or function of the part.—This reasoning

" can never betray us, if we are but sure of the

*' facts." *

The celebrated Albinus expresses himself to the

same pui-pose in his preface to Harvey's Eaercitatio

de Motu Cordis. " Incidenda autem animalia,

" quibus partes illa^ quarum actiones quasrimus

** eaedem atque homini sunt, aut- certe similes iis;

" ex quibus sine metu erroris judicare de illis ho-

" minis liceat. Quin et reliqua, si modo aliquam

" habeant ad hominem similitudinem, idonea sunt

" ad aliquod suppeditandum.'*

If Bacon had lived to read such testimonies as

these in favour of the investigation of Final Causesj

or had witnessed the discoveries to which it has led

in the study of the animal economy, he would, I

doubt not, have readily admitted, that it was not al-

together uninteresting and unprofitable, even to the

physical inquirer. Such, however, is the influence

of an illustrious name, that, in direct opposition to

the evidence of historical facts, the assertion of the

complete sterility of all these speculations is, to the

* Letter by an anonymous Correspomicnt, prefixed to Monro's

Comparative Anatomy. Loudon, 1744.


present day, repeated, with undiminished confidence,

by writers of unquestionable learning and talents.

In one of the most noted physiological works which

have lately appeared on the Continent, Bacon's

apothegm is cited more than once with unqualified

approbation ; although the author candidly owns,

that it is difficult for the most reserved philosopher

always to keep it steadily in view, in the course of

his inquiries.*

The prejudice against final causes, so generally

avowed by the most eminent philosophers of France,

during the eighteenth century, was first introduced

into that country by Descartes. It must not, how-

ever, be imagined, that, in the mind of this great

man, it arose from any bias towards atheism. Onthe contrary, he himself tells us, that his objection

to the research of uses or ends was founded entirely

on the presumptuous confidence which it seemed to

argue in the powers of human reason ; as if it were

conceivable, that the limited faculties of man could

penetrate into the counsels of Divine wisdom. Ofthe existence of God he conceived that a demon-

strative proof was afforded by the idea we are able

to form of a Being infinitely perfect, and necessarily

existing ; and it has with some probability been

conjectured, that it was his partiality to this new ar-

gument of his own, which led him to reject the

* " Je regarde, avec le grand Bacon, la philosophic des causes

" finales comme sterile: mais il est bien difficile a I'homme le

" plus reserve, de n'y avoir jamais recoursdans ses explications."

Rapports du Physique et du Moral de VHowine. Par I\I. Ic

Senateur Cabanis. Tome I. p. 352. Paris, 1805.

Sect. (). OP THE HUMAN MIND. 493

reasonings of his predecessors in support of the same

conclusion.*

To this objection of Descartes, an elaborate, and,

in my opinion, a most satisfactory reply, is to be

found in the works of Mr Boyle. The principal

scope of his essay may be collected from the follow-

ing short extract

:

*' Suppose that a countryman, being in a clear

** day brought into the garden of some famous ma-

*' thematician, should see there one of those curious

" gnomonic instruments, that shew at once the

*' place of the sun in the zodiac, his declination

" from the equator, the day of the month, the

" length of the day, &c. &c. It would indeed be

*' presumption in him, being unacquainted both with

" the mathematical disciplines, and the several in-

** tentions of the artist, to pi'etend or think himself

* " Nullas unquam rationes circa res naturales a fine quam*' Deus aut natura in iis fuciendis sibi proposuit desumemus

;

" quia non tantum debemus nobis arrogare ut ejus consiliorum

*' participes nos esse pulemus."

—

{Primip. Pars. I. §28.) ' Dum*' haec perpendo aUentius, occurrit primo non mihi esse miran-

" dum si quajdam a Deo fiant quorum rationes non intelligam

;

" nee de ejus cxistentia ideo esse dubitandum, quod forte quae*

" dam alia esse experiar quae quare, vel quomodo ab illo facta

*' sinl non comprehendo ; cum enim jam sciam naturam meam" esse valde infirraani et limitatam, Dei autem naturam esse im-

" mensam, incomprehensibilem, infinitam, ex hoc satis etiam scio

" innumerabilia ilium posse quorum causas ignorem ; atque ob

" hanc unicam rationem totuni illiid causarum genus quod afine*' feti solet in rebus physicis nullum usum habere existimo ; non

" enim absque temeritate me puto posse invcstigare fines Dei."—

•

Meditatio Quarta.

See Note (BB.)


" able to discover all the ends for which so curious

" and elaborate a piece was framed : but when he

" sees it furnished with a style, with horary lines and

" numbers, and, in short, with all the requisites of a

** sun-dial, and manifestly perceives the shadow to

*' mark from time to time the hour of the day, it

** would be no more a presumption than an error

" in him to conclude, that (whatever other uses the

** instrument was fit or was designed for) it is a

" sun-dial, that was meant to shew the hour of the

«* day." *

With this opinion of Boyle that of Newton so en-

tirely coincided, that (according to Maclaurin) he

thought the consideration of final causes essential to

true philosophy ; and was accustomed to congratu-

late himselfon the effect of" his writings in revivinsf an

attention to them, after the attempt of Descartes to

discard them from physics. On this occasion, Mac-

* In the same Essay, Mr Boyle has offered some very judi-

cious strictures on the abuses to which the research of final causes

is liable, when incautiously and presumptuously pursued. Anabstract of these, accompanied with a few illustrations from later

writers, might form an interesting chapter in a treatise of induc-

tive logic.

The subject has been since prosecuted with considerable inge-

nuity by Le Sage of Geneva, who has even attempted (and not

altogether without success) to lay down logical rules for the in-

vestigation oi ends. To this study, which he was anxious to form

into a separate science, he gave the very ill chosen name of Te-

leologie ; a name, if I am not mistaken, first suggested by WoUfius.— For some valuable fragments of his intended work with re-

spect to it, see the Account of his IJfeand Writings by his friend

M. Prevost. (Geneva, 1805.)


laurin has remarked, * that, of all sort of causes,

" final causes are the most clearly placed in our view

;

" —and that it is difficult to comprehend, why it

" should be thought arrogant to attend to the de-

" sign and contrivance that is so evidently displayed

" in nature, and obvious to all men ;—to maintain,

" for instance, that the eye was made for seeing,

" though we may not be able either to account me-" chanically for the refraction of light in its coats,

" or to explain how the image is propagated from** the retina to the mind.'* *—It is Newton's ownlanguage, however, which alone can do justice to his

sentiments on the present subject.

" The main business of natural philosophy is to

" argue from phenomena, without feigning hypo-

" theses, and to deduce causes from effects till we" come to the veiy first cause, which certainly is not

" mechanical ; and not only to unfold the me-" chanism of the world, but chiefly to resolve these

" and such like questions : Whence is it that Nature** does nothing in vain ; and whence arises all that

" order and beauty xvhich ive see in the "world ?—" How came the bodies ofanimals to be contrived

" with so much art, and for what ends xvere their

" several parts ? Was the eye contrived without

" sJdll in optics, and the ear without knowledge of" sounds /"' t

In multiplying these quotations, I am well aware

that authorities are not arguments ; but when a pre-

* AccountofNewton'sPhilosophical Discoveries, Book!,Chap. ii.

t Newton's Optics, Query SS.


judice to which authority alone has given currency

is to be combated, what other refutation is h^kely to

be effectual ?

After all, it were to be wished that the scholas-

tic -phrase^nal cause could, without affectation, be

dropped from our philosophical vocabulary ; and

some more unexceptionable mode of speaking substi-

tuted instead of it. In this elementary work, I have

not presumed to lay aside entirely a form of expres-

sion consecrated in the writings of Newton, and of

his most eminent followers ; but I am fully sensible

of its impropriety, and am not without hopes that I

may contribute something to encourage the gradual

disuse of it, by the indiscriminate employment of

the words ends and uses to convey the same idea.

Little more, perhaps, than the general adoption of

one or other of these terms is necessary, to bring

candid and reflecting minds to a uniformity of lan-

guage as well as of sentiment on the point in ques-

tion.

It was before observed, with respect to anatomists,

that all of them without exception, whether profes-

sedly friendly or hostile to the inquisition of final

causes, concur in availing themselves of its guidance

in their physiological researches. A similar remark

will be found to apply to other classes of scientific

inquirers. Whatever their speculative opinions may

be, the moment their curiosity is fairly engaged in

the pursuit of truth, either physical or moral, they

involuntarily, and often perhaps unconsciously, sub-

mit their understandings to a logic borrowed neither

from the schools of Ai'istotle nor of Bacon. The


ethical system (for example) of those ancient philo-

sophers who held that Virtue consists in following

Nature, not only involves a recognition of final

causes, but represents the study of them, in as far

as regards the ends and destination of our own

being, as the great business and duty of life.* The

system, too, of those physicians who profess to follow

Nature in the treatment of diseases, by watching

and aiding her medicative powers, assumes the same

doctrine as its fundamental principle. A still more

remarkable illustration, however, of the influence

which this species of evidence has over the belief,

even when we are the least aware of its connection

with metaphysical conclusions, occurs in the history

of the French Economical System. Of the com-

prehensive and elevated views which at first sug-

gested it, the title of Physiocratie, by which it was

early distinguished, affords a strong presumptive

proof; and the same thing is more fully demon-

strated, by the frequent recurrence made in it to

the physical and moral laws of Nature, as the uner-

ring standard which the legislator should keep in

view in all his positive institutions.! I do not speak

* " Discite. O miscri, ct cauâs cognoscite reiura,

" Quid sumus, ft quiclnam victuri gignimur."

Peusius.

Ej-w h 71 f3!i/.c/ji.ar xaTaijâdiiv tyiv fugiv, }(\ rauryj imaQc/j.

Epictet.

f " Ces lois forment ensemble cc qu'on appelle la loi nutu-

** rdle. Tous Ics hommes et toutes les puissances huniaines

" doivent etre soumis a. ces lois souveraines, instituees par I'etre

" supreme : elles sont immuables et irrefragables, et les meil-

VOL. II. I i

ELEMENTS OF THE PHILOSOPHY Chap. IV^

at present of the justness of these opinions. I wisk

only to remark, that, in the statement of them given

by their original authors, it is taken for granted as

a truth self-evident and indisputable, not merely that

benevolent design is manifested in all the physical andmoral arrangements connected with this globe, but

that the study of these arrangements is indispen-

sably necessary to lay a solid foundation for political

science.

The same principles appear to have led Mr Smith

into that train of thinking which gave birth to his

inquiries concerning National Wealth. *' Man,'*

he observes in one of his oldest manuscripts now ex-

tant, " is generally considered by statesmen and pro-

" jectors as the materials of a sort of political me-" chanics. Projectors disturb Nature in the course

" of her operations in human affairs ; and it requires

" no more than to let her alone, and give her fair

** play in the pursuit of her own designs."—And in

another passage : " Little else is requisite to carry

" a state to the highest degree of opulence from the

" lowest barbarism, but peace, easy taxes, and a

" tolerable administration of justice ; all the rest

" being brought about by the natural course of

" things. All governments which thwart this na-

" tural course ; which force things into another

" channel ; or which endeavour to arrest the pro-

** gress of society at a particular point, are un-

" leurs loix possibles; et par consequent, la base clu governe-

'< ment le plus parfait, et la regie fondamentale de toutes Ics

" loix positives ; car ics loix positives ne sent que des loix de

" manutention relatives a I'ordre naturel evidemment le plus

" avantageux au genre humain."

—

Quesnay.

\


" natural, and to support themselves are obliged to

*' be oppressive and tyrannical.'** Various other

passages of a similar import might be quoted, both

from his Wealth of Nations, and from his Theory

of Moral Sentiments.

This doctrine of Smith and Quesnay, which

tends to simplify the theory of legislation, by ex-

ploding the policy of those complicated checks and

restraints which swell the municipal codes of most

nations, has now, I believe, become the prevailing

creed of thinking men all over Europe ; and, as

commonly happens to prevailing creeds, has been

pushed by many of its partizans far beyond the views

and intentions of its original authors. Such, too, is

the effect of fashion on the one hand, and of ob-

noxious phrases on the other, that it has found some

of its most zealous abettors and propagators among

writers who would, without a moment's hesitation,

have rejected, as puerile and superstitious, any re-

ference toJinal causes in a philosophical discussion.

11.

Da?iger ofconfounding Final mth Physical Causes

i?i the Philosophy of the Human Mind,

Having said so much upon the research of Final

Causes in Physics, properly so called, I shall sub-

join a few remarks on its application to the Philoso-

phy of the Human Mind ;—a science in which the

just rules of investigation are as yet far from being

generally understood. Of this no stronger proof

* Biographical Memoirs of Smith, Robertson, and Reid, p. 100.


can be produced, than the confusion between final

and efficient causes, which perpetually recurs in the

writings of our latest and most eminent moralists.

The same confusion, as I have already observed,

prevailed in the physical reasonings of the Aristo-

telians ; but, since the time of Bacon, has been so

completely corrected, that, in the wildest theories

of modern naturalists, hardly a vestige of it is to be

traced.

To the logical error just mentioned it is owing,

that so many false accounts have been given of the

principles of human conduct, or of the motives by

which men are stimulated to action. When the ge-

neral laws of our internal frame are attentively ex-

amined, they will be found to have for their object

the happiness and improvement both of the in^

dividual and of society. This is their Final Cause,

or the end for which we may presume they were

destined by our Maker. But, in such cases, it sel-

dom happens, that, while Man is obeying the aC"

five impulses of his nature, he has any idea of the

ultimate ends which he is promoting ; or is able to

calculate the remote effects of the movements which

he impresses on the little wheels around him. These

active impulses^ therefore, may, in one sense, be

considered as the efficient causes of his conduct

;

inasmuch as they are the means employed to deter-

mine him to particular pursuits and habits ; and as

they operate (in the Jirst instance, at least) with-

out any reflection on his part on the purposes to

which they are subservient. Philosophers, however,

have in every age been extremely apt to conclude.

Sect. 6'. OF THE HUMAN MIND. 501

when they had discovered the salutary tendency of

any active principle, that it was from a sense or fore-

knowledge of this tendency that the principle de-

rived its origin. Hence have arisen the theories

which attempt to account for all our actions from

self-love ; and also those which would resolve the

whole of morality, either into political views of ge-

neral expediency, or into an enlightened regard to

our own best interests.

I do not know of any author who has been so

completely aware of this common error as Mr Smith,

In examining the principles connected with our mo-

ral constitution, he always treats separately of their

final causes, and of the mechanism (as he calls it)

by which nature accomplishes the effect ; and he has

even been at pains to point out to his successors the

great importance of attending to the distinction be-

tween these two speculations.—" In every part of

" the universe, we observe means adjusted with the

" nicest artifice to the ends which they are intend-

" ed to produce ; and in the mechanism of a plant

" or animal body, admire how everything is con-

*' trived for advancing the two great purposes of

" nature, the support of the individual, and the

** propagation of the species. But in these, and in

** all such objects, we still distinguish the efficient

*' from the final cause of their several motions and

" organizations. The digestion of the food, the

" circulation of the blood, and the secretion of the

" several juices which are drawn from it, are opera-

*.' tions all of them necessary for the great purposes


" of animal life ; yet we never endeavour to account

** for them from those purposes as from their effi-

*' cient causes, nor imagine that the blood circu-

" lates, or the food digests, of its own accord, and

" with a view or intention to the purposes of circu-

*' lation or digestion. The wheels of the watch are

" all admirably adapted to the end for which it was

" made, the pointing of the hour. All their vari-

" ous motions conspire in the nicest manner to pro-

** duce this eft'ect. If they were endowed with a

** desire and intention to produce it, they could not

" do it better. Yet we never ascribe any such inten-

** tion or desire to them, but to the watchmaker,

" and we know that they are put into motion by a

" spring, which intends the effect it produces as

" little as they do. But though, in accounting for

" the operations of bodies, we never fail to distin-

" guish, in this manner, the efficient from the final

" cause, in accounting for those of the mind, we are

" apt to confound these two different things with

*' one another. When, by natural principles, we" are led to advance those ends which a refined and

" enlightened reason would recommend to us, we** are very apt to impute to that reason, as to their

" efficient cause, the sentiments and actions by" which we advance those ends, and to imagine that

" to be the wisdom of Man, which, in reality, is the

" wisdom of God. Upon a superficial view, this

" cause seems sufficient to produce the effects which

" are ascribed to it ; and the system of Human Na-** ture seems to be more simple and agreeable, when

10


*' all its different operations are, in this manner, de-

" duced from a single principle." *

These remarks apply with peculiar force to a

theory of morals which has made much noise in our

own times ;—a theory which resolves the obligation

of all the different virtues into a sense of their utili-

ty^. At the time when Mr Smith wrote, it had been

recently brought into fashion by the ingenious and

refined disquisitions of Mr Hume ; and there can

be little doubt, that the foregoing strictures were

meant by the author as an indirect refutation of his

friend's doctrines.

The same theory (which is of a very ancient date t)

has been since revived by Mr Godwin, and by the

late excellent Dr Paley. Widely as these two

writers differ in the source whence they derive their

rule of conduct, and the saiwtions by w^hich they

enforce its observance, they are perfectly agreed

about its paramount authority over every other prin-

ciple of action. " Whatever is expedient^^^ says DrPaley, " is right. It is the utility of any moral rule

" alone which constitutes the obligation of it. t . .

" . . But then, it must be expedient on the whole,

*' at the long run, in all its effects, collateral and re-

** mote, as well as those which are immediate and

" direct ; as it is obvious, that, in computing conse-

" quences, it makes no difference in what way, or at

* Theory of Moral Sentiments, Vol. I. p. 2l6, et seq. 6th edit.

f *' Ipsa utilitas, justi prope mater et aequi."

—

Horat. Sat.

Lib. I. 3.

I Principles of Moral and Political Philosophy, Vol. L p. 70.

5 th edit.

504^ ELEMENTS OP THE PHILOSOPHY Chap. IV.

" what distance they ensue." *—^Mr Godwin has

nowhere expressed himself, on this fundamental

question of practical ethics, in terms more decided

and unqualified.

The observations quoted from Mr Smith on the

proneness of the mind, in moral speculations, to

confound together efficient and final causes, furnish

a key to the chief difficulty by which the patrons of

this specious but very dangerous system have been

misled.

Among the qualities connected witli the different

virtues, there is none more striking than their bene-

ficial influence on social happiness ; and, according-

ly, moralists of all descriptions, when employed in

enforcing particular duties, such as justice, veracity,

temperance, and the various charities of private life,

never fail to enlarge on the numerous blessings

which follow in their train. The same observation

may be applied to self-interest ; inasmuch, as the

* Ibid. p. 7^-

Tn another part of his work, Dr Paley explicitly asserts, that

(Very moral rule is liable to be superseded in particular cases

on the ground of expediency. " Moral philosophy cannot pro-

'^ nounce that any rule of morality is so rigid as to bend to no

" exceptions ; nor, on the other hand, can she comprise these

'* exceptions within any previous description. She confesses,

" that the obligation of every law depends upon its ultimate

" utility; that this utility having a finite and determinate value,

" situations may be feigned, and consequently may possibly

" arise, in which the general tendency is outweighed by the e-

" normity of the particular mischief; and of course, where ul-

" timate utility renders it as much an act of duty to break the

" rule, as it is on other occasions to observe it."—Vol. II. p. 41 1

.


most effectual way of promoting it is universally ac-

knowledged to be by a strict and habitual regard to

the obligations of morality.—In consequence of this

imity ofdcsigiiy which is not less conspicuous in the

moral than in the natural world, it is easy for a phi-

losopher to give a plausible explanation of all our

duties from one principle ; because the general ten-

dency of all of them is to determine us to the same

course of life. It does not, however, follow from

this, that it is from such a comprehensive survey of

the consequences of human conduct, that our ideas

of right and wrong are derived ; or that we are en-

titled, in particular cases, to form rules of action to

ourselves, drawn from speculative conclusions con-

cerning theJinal causes of our moral constitution.

If it be true (as some theologians have presumed to

assert) that benevolence is the sole principle of ac-

tion in the Deity, we must suppose that the duties

of veracity and justice were enjoined by Him, 7iot

on account of their intrinsic rectitude, but of their

utility : but still, with respect to man, these are sa-

cred and indispensable laws—laws which he never

transgresses, without incurring the penalties of self-

condeumation and remorse : And indeed if, without

the guidance of any internal monitor, he were left

to infer the duties incumbent on him from a calcu-

lation and comparison of remote effects, we may

venture to affirm, that there would not be enough

of virtue left in the world to hold society together.

To those who have been accustomed to reflect on

the general analogy of the human constitution, and

on the admirable adaptation of its various parts to

506 ELEMENTS OF THE PHILOSOPHY Chap. I\^.

that scene in which we are destined to act, this last

consideration will, independently of any examina-

tion of the fact, suggest a very strong presumption

a priori against tlie doctrine to which the foregoing

remarks relate. For, is it at all consonant with the

other arrangements, so wisely calculated for human

happiness, to suppose that the conduct of such a fal-

lible and short-sighted creature as Man, would be

left to be regulated by no other principle than the

private opinion of each individual concerning the

e:vpediency of his own actions ? or, in other words,

by the conjectures which he might form on the

good or evil resulting on the whole from an endless

train of future contingencies ? Were this the case,

the opinions of mankind, with respect to the rules of

morality, would be as various as their judgments

about the probable issue of the most doubtful and

difficult determinations in politics. Numberless

cases might be fancied, in which a person would not

only claim merit, but actually possess it, in conse-

quence of actions which are generally regarded with

indignation and abhorrence ;—^for, unless we admit

such duties as justice, veracity, and gratitude, to be

immediately and imperatively sanctioned by the au-

thority of reason and of conscience, it follows, as a

necessary inference, that we are bound to violate

them, whenever, by doing so, we have a prospect of

advancing any of the essential interests of society ;

or (which amounts to the same thing) that a good

end is sufficient to sanctify whatever means may ap-

pear to us to be necessary for its accomplishment.

Even men of the soundest and most penetrating un-


derstandings might frequently be led to the perpe-

tration of enormities, if they had no other light to

guide them but what they derived from their own

unceitaiu anticipations of futurity. And when we

consider how small the number of such men is, in

comparison of those whose judgments are perverted

by the prejudices of education and their own selfish

passions, it is easy to see what a scene of anarchy

the world would become. Of this, indeed, we have

too melancholy an experimental proof, in the his-

tory of those individuals who have in practice adopt-

ed the rule of general ea^pediency as their whole

code of morality ;—a rule which the most execrable

scourges of the human race have, in ail ages, pro-

fessed to follow, and of which they have uniformly

availed themselves, as an apology for their deviations

from the ordinary maxims of right and wrong.

Fortunately for mankind, the peace of society is

not thus entrusted to accident, the great rules of a

virtuous conduct being confessedly of such a nature

as to be obvious to every sincere and well-disposed

mind. And it is in a peculiar degree striking, that,

while the theory of ethics involves some of the most

abstruse questions which have ever employed the hu-

man faculties, the moral judgments and moral feel-

ings of the most distant ages and nations, with re-

spect to all the most essential duties of life, are one

and the same.*

* " Si quid rectissimum sit, quaerimus ; perspicuum est. Si

*' quid maxime expediat ; obscurum. Sin ii sumus, qui pro-

" fecto esse deberaus, ut nihil arbitremur expedire, nisi quod" rectum houestumque sit; non potest esse dubium, quid facien-

** dum nobis sit."—s-C/c. Eji, ad Fam. IV, 2.


Of this theory of utility, so strongly recommend-

ed to some by the powerful genius of Hume, and to

others by the M'ell-merited popularity of Paley, the

most satisfactory of all refutations is to be found in

Vv;^ the work of Mr Godwin. It is unnecessary to in-

' quire how far the practical lessons he has inculcated

are logically inferred from his fundamental princi-

ple ; for although I apprehend much might be ob-

jected to these, even on his own hypothesis, yet, if

such be the conclusions to which, in the judgment

of so acute a reasoner, it aj)peared to lead with de-

monstrative evidence, nothing farther is requisite to

illustrate the practical tendency of a system, which,

absolving men from the obligations imposed on them

with so commanding an authority by the moral con-

stitution of human nature, abandons every indivi-

dual to the guidance of his own narrow views concern-

ing the complicated interests of political society.*

* It is remarkable that Îr Hume, by far the ablest advocate

for the theory in question, has indirectly acknowledged its in.

consistence with some of the most important facts which it pro-

fesses to explain. " Though the heart" he observes in the 5th sec-

tion of his Inquiry concerning Morals, " takes not part entirely

" with those general notions, nor regulates all its love and hatred

" by the universal abstract differences of vice and virtue, without

" regard to self, and the persons with whom we are more inti-

" mately connected;yet have these moral differences a cohsi-

" derable influence, and being sufficient, at least, for discourse,

" serve all the purposes in company, on the theatre, and in the

" schools."—On this passage, the following very curious note is

to be found at the end of the volume ; a note (by the way)

which deserves to be added to the other proofs already given of

the irresistible influence which the doctrine of final causes occa-

sionally exercises over the most sceptical minds. " It is imdy


One very obvious consideration seems to have en-

tirely escaped the notice of this, as well as of many

other late inquirers : That, in ethical researches,

not less than in those which relate to the material

universe, the business of the philosopher is limited

to the analytical investigation of general laws from

the observed phenomena •, and that if, in any in-

stance, his conclusions should be found inconsistent

with acknowledged facts, the former must necessa-

rily be corrected or modified by the latter. Onsuch occasions, the ultimate appeal must be always

made to the moral sentiments and emotions of the

human race. The representations, for example,

which we read with so much delight, in those poets,

of whatever age and country, who have most suc-

cessfully touched the human heart ;—'Of the heroi-

eal sacrifices made to gratitude, to parental duty, to

filial piety, to conjugal affection ;—are not amena-

ble to the authority of any ethical theory, but are

the most authentic records of the phenomena which

it is the object of such theories to generalize. The.

sentiment of Publius Syrus

—

Omne dia:eris maledic-

** ordained by nature, that private connections should commonly

^' prevail over universal views and considerations ; otherwise our

" affections and actions would be dissipated and lost, for want of

" a proper limited object."—Does not this remark imply an ac-

knowledgment, First, That the principle of general expediency

(the sole principle of virtuous conduct, according to Mr iiume,

in our most important transactions with our fellow-creatures)

would not contribute to the happiness of society, if men should

commonly act upon it; and, Secondly, That some provision is

made in our moral constitution, that we shall, in fact, be influen-

ced by other motives in discharging the offices of private life?


turn, quum ingratum hominem c?e>er/.9—speaks a

language which accords with every feeling of an un-

perverted mind ;—it speaks the Language of Nature,

which it is the province of the moralist, not to criti-

cise, but to listen to with reverence. By employ-

ing our reason to interpret and to obey this, and

the other moral suggestions of the heart, we may

trust with confidence, that we take the most effec-

tual means in our power to augment the sum of hu-

man happiness ;—but the discovery of this connec-

tion between virtue and utility is the slow result of

extensive and philosophical combinations ; and it

would soon cease to have a foundation in truth, if

men were to substitute their own conceptions of ex-

pediency, instead of those rules of action which are

inspired by the wisdom of God.*

It must not be concluded from the foregoing ob-

servations, that, even in ethical inquiries, the con-

sideration of final causes is to be rejected. On the

contrary, Mr Smith himself, whose logical precepts

on this subject I have now been endeavouring to il-

lustrate and enforce, has frequently indulged his cu-

riosity in speculations about ufês or advantages

;

and seems plainly to have considered them as im-

portant objects of philosophical study, not less than

efficient causes. The only caution to be observed

is, that the one may not be confounded with the

other.

Between these two different researches, however,

there is, both in physics and ethics, a very intimate

* See Note (CC.)


connection. In various cases, the consideration of

final causes has led to the discoveiy of some general

law of nature ; and, in ahnost every case, the disco-

very of a general law clearly points out some wise

and beneficent purposes to which it is subservient.

Indeed, it is chiefly the prospect of such applications

which renders the investigation of general laws in-

teresting to the mind. *

* See Note (DD.)


CONCLUSION OF PART SECOND.

In the foregoing chapters of this Second Part, I

have endeavoured to turn the attention of my readers

to various important questions relating to the Hu-

man Understanding ; aiming, in the first place, to

correct some fundamental errors in the theories com-

monly received with respect to the powers of intui-

tion and of reasoning ; and, secondly, to illustrate

some doctrines connected with the ground-work of

the inductive logic, which have been either overlook-

ed, or misapprehended by the generality of preced-

incf writers. The bulk to which the volume has al-

ready extended, renders it impossible for me now to

attempt a detailed recapitulation of its contents :

—

Nor do I much regret the necessity of this omission,

having endeavoured, in every instance, as far as I

could, to enable the intelligent reader to trace the

thread of my discussions.

In a work professedly elementary, the frequent

references made to the opinions of others may, at

first sight, appear out of place ; and it may not un-

naturally be thought, that I have too often indulged

in critical strictures, where I ought to have confined

myself to a didactic exposition of first principles.

To this objection I have only to reply, that my aim

is not to supplant any of the established branches of

academical study ; but, by inviting and encouraging

the young philosopher, when his academical career


is closed, to review, with attention and candour, liis

past acquisitions, to put him in the way of supplying

what is defective in the present systems of education.

I have accordingly entitled my book. Elements—not

of Logic or of Pneumatology, but—of the Philoso-

phy of the Human Mind ; a study which, according

to my id(â of it, presupposes a general acquaintance

with the particular departments of literature and of

science, but to which I do not know that any ele-

mentary introduction has yet been attempted. It is

a study, indeed, whereof little more perhaps than

ihe elements can be communicated by the mind of

one individual to that of another.

In proof of this, it is sufficient here to hint (for

I must not at present enlarge on so extensive a to^

pic), that a knowledge of the general laws which re-

gulate the intellectual phenomena is, to the logical

student, of little practical value, but as a preparation

for the study of Himself. In this respect, the ana-

tomy of the mind differs essentially from that of the

body ; the structure of the former (whatever colla-

teral aids may be derived from observing the varie-

ties of genius in our fellow-creatures) being accessi-

ble to those 'alone who can retire into the deepest

recesses of their own internal frame ; and even to

tJiese presenting, along with the generic attributes

of the race, many of the specific peculiarities of the

individual. On this subject every writer, whose

speculations are at all worthy of notice, must draw

his chief materials from within ; and it is only by

comparing the conclusions of different writers, and

VOL. n. K k

514> ELEMENTS OF THE PHILOSOPHY

subjecting all of them to the test of our personal ex-

perience, that we can hope to separate the essential

principles of the human constitution from the unsus-

pected effects of education and of temperament j*

or to apply with ad^ântage, to our particular circum-

stances, the combined results of our reading and of

our reflections. The constant appeal which, in such

inquiries, the reader is thus forced to make to his

own consciousness and to his own judgment, has a

powerful tendency to form a habit, not more essen-

tial to the success of his metaphysical researches,

than of all his other speculative pursuits.

Nearly connected with this habit, is a propensity

to weigh and to ascertain the exact import of words ;

one of the nicest and most difficult of all analytical

processes ; and //z«^ upon which more stress has been

' justly laid by our best modern logicians, than upon

any other organ for the investigation of truth. For

« the culture of this propensity, no science is so pe-

culiarly calculated to prepare the mind, as the study

of its own operations. Here, the imperfections of

words constitute the principal obstacle to our pro-

gress ; nor is it possible to advance a single step,

without struggling against the associations imposed

by the illusions of metaphorical terms, and of ana-

* I use the word tcmpcramcjit, in this instance, as synonymous

witli X.\ividiosijnfiasi/ of medical authors; a term which I thought

mii^ht have savoured of affectation if apphed to i/ie mind ; al-

tliough authorities for such an emphiyment of it lire not want-

ing among old English writers. One example, directly in point,

is quoted by Johu'^nn from Glanville. " The understanding

" also hath its idiosi/iicracits, as well as other faculties."


logical theories. Abstracting, therefore, from its

various practical applications, and considering it

merely as a gymnastic exercise to the reasoning

powers, this study seems pointed out by nature as

the best of all schools for inuring the undersUmd-

ing to a cautious and skilful employment of lan-

guage as the instrument of thought.

The two first chapters of this volume relate to lo-

gical questions, on which the established opinions

appear to me to present stumbling-blocks at the very

threshold of the science. In treating of these, I

have canvassed with freedom, but, I hope, v^îth due

respect, the doctrines of some illustrious moderns,

whom I am proud to acknowledge as my masters ;

of those, more particularly, whose works are in the

highest repute in our British Universities, and whose

errors I was, on that account, the most solicitous to

rectify. For the space allotted to my criticisms on

Condillac, no apology is necessary to tliose who

have the slightest acquaintance with the present

state of philosophy on the Continent, or who have

remarked the growing popularity, in this Island, of

some of his weakest and most exceptionable theories.

—On various controverted points connected with ,.

the theory of evidence, both demonstrative and ex- 4-

perimental, I trust, with some confidence, that I "V

shall be found to have thrown considerable light

:

in other instances, I have been forced to content

myself with proposing my doubts ; leaving the task

of solving them to future inquirers. To awaken a

dormant spirit of discussion, by pointing out the im-

perfections of generally received systems, is at least


one step gained towards the farther advancement of

knowledge.

It is justly and philosophically remarked by Burke,

that " nothing tends more to the corruption of

" science than to suffer it to stagnate. These wa-

" ters must be troubled before they can exert their

" virtues. A man who works beyond the surface

*' of things, though he may be wrong himself, yet

*' he clears the way for others, and may chance to

" make even his errors subservient to the cause of

" truth." *

The subsequent chapters, relative to the Baco-

nian Logic, bear, all of them, more or less, in their

general scope, on the theory of the intellectual

powers, and on the first principles of human know-

ledge. In this part of my work, the reader will

easily perceive, that I do not pi'ofess to deliver logi-

cal precepts ; but to concentrate, and to reflect back

on the Philosophy of the Mind, whatever scattered

lights I have been able to collect from the experi-

mental researches to which that Philosophy has given

birth. I have aimed, at the same time (and I hoj)e

not altogether without success), to give somewhat

more of precision to the technical phraseology of

the Baconian school, and of correctness to their me-

taphysical ideas.

Before concluding these speculations, it may not

be improper to caution my readers against suppo-

sing, that when I speak of the Baconian school, or

of the Baconian logic, I mean to ascribe entirely to

the Novum Organon the advances made in physi-

* Inquiry into the Sublime and Ceauliful, Part L Sect. xix.


cal science, since the period of its publication. The

singular effects of this, and of the other inestimable

writings of the same author, in forwarding the sub-

sequent progress of scientific discovery, certainly en-

title his name, far more than that of any other in-

dividual, to be applied as a distinguishing epithet to

the modern rules of philosophizing ; but (as I have

elsewhere observed) " the genius and writings of

" Bacon himself were powerfully influenced by the

** circumstances and character of his age : Nor can

" there be a doubt, that he only accelerated a revo-

" lution which was already prepared by many con-

" current causes." *—My reasons for thinking so,

which rest chiefly on historical retrospects, altoge-

ther foreign to my present design, I must delay

stating till another opportunity.

To this observation it is of still greater import-

ance to add, that, in contrasting the spirit and the

utility of the new logic with those of the old, I have

no wish to see the former substituted, in our uni-

versities, in room of the latter. By a strange in-

version in the order of instruction. Logic, instead of

occupying its natural place at the close of the aca-

demical course, has always been considered as an in-

troduction to the study of the sciences ; and has,

accordingly, been obtruded on the uninformed

minds of youth, at their first entrance into the

schools. While the syllogistic art maintained its

reputation, this inversion was probably attended

with little practical inconvenience ; the trite and

puerile examples commonly resorted to for the illus-

* Outlines of Moral Philosophy, first printed in 1793.

518 ELEMENTS OP THE PHILOSOPHY

tration of its rules, presupposing a very slender

stock of scientific attainments : but now, when the

word Logic is universally understood in a more ex-

tensive sense, as comprehending, along with an out-

line of Aristotle's Ot'gano?!, some account of the

doctrines' of Bacon, of Locke, and of their succes-

sors, it seems indispensably necessary that this

branch of education should be delayed till the un-

derstanding has acquired a wider and more varied

range of ideas, and till the power of reflection (the

last of our faculties which nature unfolds) begins to

solicit its appropriate nourishment. What notions

can be annexed to such words as analysis, synthesis,

induction, experience, analogy, hypothetical and le-

gitimate theories, demonstrative and moral certainty,

by those whose attention has hitherto been exclusive-

ly devoted to the pursuits of classical learning ? Afluent command, indeed, of this technical phraseo-

logy may be easily communicated ; but it would be

difficult to devise a more effectual expedient for

misleading, at the very outset of life, the inexpe-

rienced and unassured judgment. The perusal of

Bacon's writino:s, in particular, disfigured as they

are by the frequent use of quaint and barbarous ex-

pressions, suited to the scholastic taste of his con-

temporaries, ought to be carefully reserved for a

riper age.*

* Ilaller mentions, in his Elements of Physiology, that he was

forcfd to enter on the study of logic in the tenth year of his age.

" jNIemini me annum natum decimum, quo avidus historiam et

" poe&in devorassem, ad loH,icam, et ad Claueeugianam logi-

" cam ediscendam coactum fuissc, qua nihil poterat esse, pro

6


In confirmation of this last remark, many addi-

tional arguments might be drawn from the peculiar

circumstances in which Bacon wrote. At the pe-

riod when he entered on his literary career, various

branches of physical science were already beginning

to exhibit the most favourable presages of future

improvement ; strongly inviting his original and

powerful mind to co-operate in the reformation of phi-

losophy. The turn of his genius fortunately led him

to employ himself chieiiy in general suggestions for

the advancement of learning ; and, leaving to others

the task of inductive investigation, to aim rather at

stating such rules as might direct and systematize

their exertions. In his own experimental researches

he was not very fortunate ; nor is much reliance to

be placed on the facts recorded in his Histories.

Perhaps the comprehensiveness of his views dimi-

nished his curiosity with respect to the particular

objects of science j or, perhaps, he found the mul-

" hujusmodi homuncione, sterilius." (Tomus VIII, Pars Secun-

da, p. 24. Lausannae, 1778.) It seems difficult to imagine any

attempt more extravagant than that of instructing a child, only

ten years old, in the logic of the schools ; and yet it is by no means

a task so completely impracticable as to convoy to a pupil, al-

together uninitiated in the Elements of Physics, a distinct idea

of the object and rules of the Novum Ori'ânon.

The example of Mr Smith, during the short time he held the

Professorship of hoîc at Glasgow, is wortliy of imitation in

those universities which admit of similar deviations from old

practices. For an account of his plan, see Biographical Me-

moirs of Smith, Robertson, and Reid, p. 12 ; where I have in-

serted a slight but masterly sketch of his academical labours,

communicated to me by his pupil and friend, the late Mr Millar.

5S0 ELEMENTS OF THE PHILOSOPHY

'tiplicity of his engagements in active life, more cott^

sistent with speculations, in which the chief ma-

terials of his reasonings were to be drawn from his

own reflections, than with inquiries which demanded

an accurate observation of external phenomena, or a

minute attention to experimental processes. In this

respect, he has been compared to the Legislator of

the Jews, who conducted his followers within sight

of their destined inheritance ; and enjoyed, in dis-

tant prospect, that promised land which he himself

was not permitted to enter.*

The effect of this prophetic imagination in cloth-

ing his ideas, to a greater degree than a severe lo-

gician may approve, with the glowing colours of a

* See Cowley's Ode, prefixed to Sprat's History of the Royal

Society.

Nor does Bacon himself seem to have been at all disposed to

overrate the value of his own contributions to Experimental

Science. " In rebus quibuscunque difHcilioribus," he has observ-

ed on one occasion, " non expectandum est ut quis simul et serat

" et nietat ; sed prsparatione opus est, ut per gradus inatu-

" rescant." But the most remarkable passage of this sort, which

I recollect in his writings, occurs towards the close of his great

work, Dc Aiigmeniis Scientiarum ;—" Tandem igitur paululuni

" respirantes, atque ad ea, quaj prajtervecti sumus, oculos re-

" flectentcs, hunc tractatuni nostrum non absimilem esse cense-

" mus sonis illis et praeludiis, quae praetentant Musici, dum fides

"ad modulaiionem concinnant: Quae ipsa quidem auribus in-

" gratum quiddam et asperum cxhibcnt; at in causa sunt, ut

" quae sequmitur omnia sint suaviora : Sic nimirum nos in ani-

" mum induximus, ut in cithara Musarum concinnanda, et ad

*' harmoniam veram redigenda, operam navaremus, quo ab aliis

" postea pulsentur chordce, meliore digito, aut plcctro."

4 Bacon.

OF THE HUMAN MIND. 5f1

poetical diction, was unavoidable. The wonder is,

that his style is so seldom chargeable with vagueness

and obscurity ; aad that he has been able to be-

queath to posterity so many cardinal and eternal

truths, to which tlie progressive light of science is

every day adding a new accession of lustre. Ofthese

truths, however, (invaluable in themselves as heads

or texts, pregnant with thought) many,—to borrow

the expression of a Greek poet,

—

sound only to the

intelUgent ; while others present those confident but

indefinite anticipations of intellectual regions yet un-

discovered, which, though admirably calculated to

keep alive and to nourish the ardour of the man of

science, are more fitted to awaken the enthusiasm,

than to direct the studies of youth. Some of them,

at the same time (and these, I apprehend, cannot

be too early impressed on the memory), are singu-

larly adapted to enlarge and to elevate the concep-

tions ; exhibiting those magnificent views of know-

ledge which, by identifying its progress with the

enlargement of human power and of human happi-

ness, ennoble the humblest exertions of literary in-

dustry, and annihilate, before the triumphs of genius,

the most dazzling objects of vulgar ambition.—A ju-

dicious selection of such passages, and of some ge-

neral and striking aphorisms from the Novum Or-

ganon, would form a useful manual for animating

the academical tasks of the student ; and for gra-

dually conducting him from the level of the subor-

dinate sciences, to the va?itage-ground of a higher

philosophy.

Unwilling as I am to touch on a topic so hopeless

5^2 ELEMENTS OF THE PHILOSOPHY, &C.

as that of Academical Reform, I camiot dismiss this

subject, without remarking, as ^fact which, at some

future period, will figure in literary history, that two

hundred years after the date of Bacon's philosophi-

cal works, the antiquated routine of study, originally

prescribed in times of scholastic barbarism and of

popish superstition, should, in so many Universities,

be still suffered to stand in the way of improvements,

recommended at once by the present state of the

sciences, and by the order which nature follows in

developing the intellectual faculties. On this sub-

ject, however, I forbear to enlarge.—Obstacles of

which I am not aware may perhaps render any con-

siderable innovations impracticable ; and, in the

mean time, it would be vain to speculate on ideal

projects, while the prospect of realizing them is so

distant and uncertain.

NOTES AND ILLUSTRATIONS.

NOTES AND ILLUSTRATIONS,

Note (A.) p. 40.

Of the fault in Euclid's arrangement which I have here re-

marked, some of the ancient editors were plainly aware, as they

removed the two theorems in question from the class of axioms,

and placed them, with at least an equal impropriety, in that of

postulates. '' In quibusdam codicibus,'' says Dr Gregory,

" Axiomata 10 et 11 inter postulata numerantur,"

—

Euclidis

quce supersunt omnia. Ex Recens. Dav. Gregorii. Oxon. 1703,

p. S.

The 8th Axiom too in Euclid's enumeration is evidently out

of its proper place. Ka/ ra, i(paon,o'Q>vra sff aXkTika isa, aXX^jXo/ff

scT; :—thus translated by Dr Simson ;*' Magnitudes which co-

" incide with one another, that is, which exactly fill the same

" space, are equal to one another." This, in truth, is not an

axiom, but a definition. It is the definition of geometrical equa-

lity ;—the fundamental principle upon which the comparison of

all geometrical magnitudes will be found ultimately to depend.

For some of these slight logical defects in the arrangement of

Euclid's definitions and axioms, an ingenious, and, I think, a

solid apology, has been offered by M. Prevost, in his Essais de

Philosophic. According to this author (if I rightly understand

his meaning), Euclid was himself fully aware of the objections

to which tliis part of his work is liable ; but found it impossible

to obviate them, without incurring the still greater inconveni-

ence of either departing from those modes of proof which he

526 NOTES AND ILLUSTRATIONS.

had resolved to employ exclusively in the composition of his

Elements ;* or of revolting the student, at his first outset, by

prolix and circuitous demonstrations of manifest and indispu-

table truths.—I shall distinguish by Italics, in the following

quotation, the clauses to which I wish more particularly to di-

rect the attention of my readers.

*' C'est done I'imperfection (peut-etre inevitable) de nos

*' conceptions, qui a engage a faire entrer les axiomes pour

" quelque chose dans les principes des sciences de raisonne-

" ment pur. Et ils y font un double office. Les uns rempla-

*' cent des definitions. Les autres remplacent des propositions

'' susceptibles d'etre demontrês. J'en donnerai des exemples

" tires des Elemens d'Euclide.

*' Les axiomes remplacent quelquefois des definitions tres

" faciles a faire, comme celle du motôM^. (El. Ax. 9.) D'autres" suppleent a certaines definitions difficiles et qu'on evite, comme

" celles de la ligne droite et de Vangle.

" Quelques axiomes remplacent des theoremes. J'ignore si

" (dans les principes d'Euclide) I'axiome 11. peut-etre de-

" montre (comme I'ont cru Proclus et tant d'autres anciens

" et modernes). S'il j)eut Vetre, cet axiome supplee a une

*' demonstration 2'>yohablement laboricuse.

" Puisqvie les axiomes ne font autre office que suppleer a

" des definitions et a des theoremes, on demandera peut-etre

" qu'on s'en passe. Observons 1. Qjiils evitent souvent des

" longueurs inutiles. 2. Qu'ils tranchent les disputes a I'epoqiie

*' meme ou la science est imparfaite. S. Que s'il est un etat,

*' auquel la science puisse s*en passer (ce queje nqffirmc point)

" il est du moins sage, et meme indispensable, de les employert

" taut que quelque insujpsance, dans ce degrt de perfectiofi oil

" I'on tend, interdit un ordre absohnmnt irr^prochable. Ajoutons

" 4. Que dans chaque science il y a ordinairement un principe

" qu'on pourroit appeller dominant, et qui par cette raison

'< seule (et independamment de cellos que je viens d'alleguer) a

" paru devoir etrc sorti, pour ainsi dire, du champ des defini-

* By intiodiicin?, for example, tlie idea 0^ Motion, which he has stuiiicd

to avoid, as much as possible, in delivering the EUnnenls of Plane Geo-

metry.

NOTES AND ILLUSTRATIONS. 527*' tions pour etre mis en vue sous forme d'axiome. Tel me** paroit etre en geometric le principe de eongruence contenu

" dans le 8 Axiome d'Euclide."

—

Esuaia de Philosophie, Tom.

II. pp. 30, 31, 32.

These remarks go far, in my opinion, towards a justifica-

tion of Euclid for the latitude with which he has used the

word axiom in his Elements. As in treating, however, of the

fundamental laws of human belief, the utmost possible preci-

sion of language is indispensably necessary, I must beg leave

once more to remind my readers, that, in denying Axioms to be

the first principles of reasoning in mathematics, I restrict the

meaning of that word to such as are analogous to the first seven

in Euclid's list. Locke, in what he has written on the subject,

has plainly understood the word in the same limited sense.

Note (B.) p. 73.

The prevâlence in India of an opinion bearing some resem-

blance to the Berkeleian Theory, may be urged as an ohjoc-

tion to the reasoning in the text ; but the fact is, that this re-

semblance is much slighter than has been generally appre-

hended. (See Philosophical Essays, pp. 81, 82, et sccj.) Onthis point the following passage from Sir William Jones is de-

cisive ; and the more so, as he himself has fallen into the com-

mon mistake of identifying the Hindu Belief with the conclu-

sions of Berkeley and Hume." The fundamental tenet of the Vtdanti school cdnsisted,

" not in denying the existence of matter, that is, oj"solidity, im-

" peyietrability, and extended Jigurc (to deny which tvoidd be

" lunacyJ, hid in correcting the popular notion of it, and in con-

" tending, that it has no essence independent of mental per-

" ception, that existence and perceptibility are convertible

" terms, that external appearances and sensations are illusory,

" and tvoidd vanish into nothing, ij the divine energy, tv/iich

" alone sustains them, were suspended but Jbr a moment;^ aa

* Sir William Jones here evidently confoniids the system which repie-

sents the material iinivtrse as not only at first created, but as every mo-

ment upheld by the agen<y of Divine Power, with that of Berkeley and

Hume, which, denying the distinction between prininy and scccuiary qua-


" opinion which Epicharmus and Plato seem to have adopted,

" and which has been maintained in the present century with

" great elegance, but with little public applause ;partly be-

" cause it has been misunderstood, and partly because it has

" been misapplied by the false reasoning of some unpopu-

" lar writers, who are said to have disbelieved in the mo-** ral attributes of God, whose omnipresence, v/isdom, and

" goodness, are the basis of the Indian philosophy. I have

" not sufficient evidence on the subject to profess a belief in

** the doctrine of the Vedanta, which human reason alone

" could, perhaps, neither fully demonstrate, nor fully disprove ;

*' but it is manifest, that nothing can be farther removed from

" impiety than a system wholly built on the purest devotion."

— Works of Sir William Jones, Vol. I. pp. l65, \66.

From these observations (in some of which I must be per-

mitted to say, there is a good deal of indistinctness, and even

of contradiction), it may on the whole be inferred, 1. That in

the tenets of the Vedanti school, however different from the

first apprehensions of the unreflecting mind, there was nothing

inconsistent with the fundamental laws of human belief, any

more than in the doctrine of Copernicus concerning the earth's

motion. 2. That these tenets were rather articles of a theo-

logical creed, than of a philosophical system ; or, at least, that

the two were so blended together, as sufficiently to account for

the hold which, independently of any refined reasoning, they

had taken of the popular belief.

In this last conclusion I am strongly confirmed, by a letter

which I had the pleasure of receiving, a few years ago, from

my friend Sir James Mackintosh, then Recorder of Bombay.

His good natui-e will, I trust, pardon the liberty I take in men-

tioning his name upon the present occasion, as 1 wish to add

to the following very curious extract, the authority of so en-

litics, asserts, that extension, fijiure, anrl impenetrability, are not less incon-

ceivable wiliioul a percipient mind, than (;ur sensations of beat and cold,

sounds and odours. Accoiding to both systems, it niisy nndoubli dlv be said,

that the material universe iias no existence independent of mind; but it

ought not to be overlooked, tliat in the one, tiiis word refers lo the Creator,

and in the other^ to the created percipient.

NOTES AND ILLUSTRATIONS. 529

lightened and philosophical an observer.—Amidst the variety

of his other important engagements, it is to be hoped that the

results of his literary researches and speculations, while in the

East, will not be lost to the world.

" I had yesterday a conversation with a young

*• Bramin of no great learning, the son of the Pundit (or asses-

*' sor for Hindu law) of my Court. He told me, that, besides

" the myriads of gods whom their creed admits, there was one

" whom they know by the name of Brim, or the gi-eat one,

*' without form or limits, whom no created intellect could make" any approach towards conceiving ; that, in reality, there

" were no trees, no houses, no land, no sea, but all without

*' was Maia, or illusion, the act of Brim ; that whatever we" saw or felt was only a dream, or, as he expressed it in his

** imperfect English, thinking in one's sleep, and that the re-

" union of the soul to Brim, from whom it originally sprung,

" was the awakening from the long sleep of finite existence.

" All this you have heard and read before as Hindu specula-

" tion. What struck me was, that speculations so refined and

" abstruse should, in a long course of ages, have fallen through

" so great a space as that which separates the genius of their

*' original inventor from the mind of this weak and unlettered

" man. The names of these inventors have perished ; but their

" ingenious and beautiful theories, blended with the most mon-

" strous superstitions, have descended to men very little exalt-

" ed above the most ignorant populace, and are adopted by

" them as a sort of articles of faith, without a suspicion of their

" philosophical origin, and without the possibility of compre-

" bending any part of the premises from which they were de-

" duced. I intend to investigate a little the history of these

*' opinions, for 1 am not altogether without apprehension, that

*' we may all the while be mistaking the hyperbolical effusions

" of mystical piety, for the technical language of a philoso-

*• phical S3'stera. Nothing is more usual than for fervent

" devotion to dwell so long and so warmly on the mean-" ness and worthlessness of created things, and on the all-suf-

'' ficiency of the 3upreme Being, that it slides insensibly from

OL. ir. hi


" comparative to absolute language, and, in the eagerness of

" its zeal to magnify the Deity, seems to annihilate everything

" else. To distinguish between the very different import of

" the same words in the mouth of a mystic and of a sceptic, re-

" quires more philosophical discrimination than most of our

" Sanscrit investigators have hitherto shewn."

Note (C.) p. 85.

The private correspondence here alluded to was between

Mr Hume and the late Sir Gilbert Elliott ; a gentleman who

seems to have united, with his other well-known talents and

accomplishments, a taste for abstract disquisitions, which rare-

ly occurs in men of the world ; accompanied with that sound-

ness and temperance ofjudgment which, in such researches,

are so indispensably necessary to guard the mind against the

illusions engendered by its own subtility. In one of his let-

ters (of which the original draft, in his own hand-writing, was

communicated to me by the Earl of Minto) he expresses

himself thus :*

. . . " I admit, that there is no writing or talkipg of any

" subject which is of importance enough to become the ob-

*' ject of reasoning, without having recourse to some degree of

" subtilty and refinement. The only question is, where to stop,

'* how far we can go, and why no farther ? To this question

" I should be extremely happy to receive a satisfactory an-

" swer. I can't tell if I shall rightly express what I have just

" now in my mind ; but I often imagine to myself, that I per-

" ceive within me a certain instinctive feeling, which shoves

" a'>ay at once all over subtile refinements, and tells me, with

" authority, that these air-built notions are inconsistent with

" life and experience, and by consequence cannot be true or

" solid. From this I am led to think, that the speculative prin-

" ciples of our nature ought to go hand in hand with the prac-

" tical ones ; and, for my own part, when the former are so far

" pushed, as to leave the latter quite out of sight, I am always

" apt to suspect that we have transgressed our limits. If it

" should be asked, how far will these practical principles go ?

* The letter is dated in 1751.


*' I can only answer, that tlie former difficulty will recur, un-

" less it be found, that there is something in the intellectual

" part of our nature, resembling the moral sentiment in the

" moral part of our nature, which determines this, as it were,

" instinctively. Very possibly 1 have wrote nonsense : How-

" ever, this notion first occurred to me at London, in conver-

" sation with a man of soiTie depth of thinking ; and talking

" of it since to your friend Henry Home, * I found that he

" seemed to entertain some notions nearly of the same kind,

" and to have pushed them much farther."

The practical principles referred to in this extract, seem to

me to correspond very nearly with what I have called funda-

mental Iaxvs of belief, ovfrst elements ofhuman reason ; and the

SOMETHING in the intellectual part of our nature, resembling

the moral sentiment in the moral part of our nature, is plainly

descriptive of what Reid and others have since called common

sense ;—coinciding, too, in substance with the philosophy of

Lord Kames, who refers our belief of the existence of the

Deity, and of various other primary truths, to particular senses,

forming a constituent part of our intellectual frame. I do not

take upon me to defend the forms of expression which Mr

Hume's very ingenious correspondent has employed to convey

his ideas ; and which, it is probable, he did not think it neces-

sary for him, in addressing a confidential friend, to weigh with

critical exactness ; but his doctrine must be allowed to approxi-

mate remarkably to those parts of the works of Reid^ where he

appeals from the paradoxical conclusions of metaphysicians, to

the principles on which men are compelled, by the constitu-

tion of their nature, to judge and to act in the ordinary con-

cerns of life ;—as well as to various appeals of the same kind,

which occur in Lord Karnes's writings. My principal object,

however, in introducing it here, was to shew, that this doc-

trine was the natural result of the state of science at the period

when Reid appeared ; and, consequently, that no argument

against his originality in adopting it can reasonably be found-

ed on a coincidence between his views concerning it and those

of any preceding author.

* Afterwards Lord Kames.


Of Mr Hume's respect for the literary attainments of thl«

correspondent, so strong a proof occurs in a letter (dated

Ninewells, March 10, 1751), that I am tempted to subjoin

to the foregoing quotation the passage to which I allude.

" You would perceive, by the sample I have given you, that

" I make Cleanthes the hero of the dialogue. Whatever you" can think of to strengthen that side of the argument, will be

" most acceptable to me. Any propensity you imagine I have

" to the other side crept in upon me against my will ; and 'tis

** not long ago that I burned an old manuscript-book, wrote

" before I was twenty, which contained, page after page, the

** gradual progress of my thoughts on that head. It began

" with an anxious search after arguments to confirm the com-

" mon opinion : Doubts stole in,—dissipated,—returned,

—

*' were again dissipated,-—returned again : And it was a per-

" petual struggle of a restless imagination against inclination^

" perhaps against reason.

" I have often thought, that the best way of composing a*' dialogue would be, for two persons that are of different opi-

" nions about any question of importance, to write alternately

" the different parts of the discourse, and reply to each other.

*' By this means that vulgar error would be avoided, of put-

" ting nothing but nonsense into the mouth of the adversary ;

" and, at the same time, a variety of character and genius

*' being upheld, would make the whole look more natural and

" unaffected. Had it been my good fortune to live near you,

" I should have taken upon me the character of Philo in the

" dialogue, which you'll own I could have supported natural-

" ]y enough : and j'ou would not have been averse to that of

*' Cleanthes."

In a postscript to this letter, Mr Hume recurs to the same

idea. " If you'll be persuaded to assist me in supporting Cle-

" anthes, I fancy you need not take the matter any higher

*' than Part 3. He allows, indeed, in Part 2, that all our in-

*' ference is founded on the similitude of the works of nature

" to the usual effects of mind : otherwise they must appear a

" mere chaos. The only difficulty is, why the other dissimili-

" tudes do not weaken the argument : And, indeed, it would

NOTES AND ILLUSTRATIONS. 589* seem from experience and feeling, that they do not weaken*' it so much as we might reasonably expect. A theory to

" solve tliis would be very acceptable." *

Note (D.) p. 92.

It would perhaps be difficult to mention another phrase in

our language which admits of so great a variety of interpreta-

tions as (^rnmon sense, and to which, of cousequence, it could

have been equally dangerous to annex a new technical meaning

in stating a controversial argument. Dr Beattie has enume-

rated some of these in the beginning of his Essay, but he has

by no means exhausted the subject ; nor is his enumeration

altogether unexceptionable in point of logical distinctness. Onthis point, however, 1 must allow my readers to judge for

themselves.—See Essay on the Nature and Immutability of

Truth, p. 37, ei serj. 2d edit.

The Latin phrase sensus communis has also been used with

much latitude. In various passages of Cicero it may be per-

fectly translated by the English phrase common sense ; and, in

the same iieceptation, it is often employed in modern latinity.

Of this (not to mention other authorities) many examples oc-

cur in the Lectiones Mathematicce of Dr Barrow ; a work not

more distinguished by originality and depth of thought, than

by a logical precision of expression. In one of these, he ap-

peals to common sense (sensus communis) , in proof of the cir-

cumference of the circle being less than the perimeter of the

circumscribed square.—Lect. 1.

On other occasions, the sensus communis of classical writers

plainly means something widely different ;—as in those noted

lines ofJuvenal, so ingeniously ill u&trated by Lord Shaftesbury,

in his Essay on the Freedom of Wit and Humour.

*• Haec satis ad juvenem, quern nobis fama superbiim

" Tradit, et inflatum, plenumque Neione propioquo.

** Rarus enira terme sensus communis in ilia

" Fortuna."

*' Some commentators," says Shaftesbury, ** interpret this

• From the above quotations il appears, that Mr Hume's posthumous

work, entitled Dialogues concernins; Natural Religion, was projected, acdj

w part at least, executed, tweuty-five years bef«re his death.

534f NOTES AND ILLUSTRATIONS.

" very differently from what is generally apprehended. They*' make this common sense of the poet, by a Greek derivation,

" to signify sense of public weal, and of the common interest

;

" love of the community or society, natural affection, humani-

" ty, obligingness, or that sort of civility which rises from a

"just sense of the common rights of mankind, and the natural

" equality there is among those of the same species.

" And, indeed, if we consider the thing nicely, it must seem

" somewhat hard in the poet to have deny'd wit or ability to a

" court such as that of Rome, even under a Tiberius or a

" Nero. But for humanity or sense of public good, and the

" common interest of mankind, 'twas no such deep satire to

" question whether this was properly the spirit of a court.

•* 'Twas difficult to apprehend what Community subsisted

" among courtiers ; or what Public among an absolute Prince

" and his slave-subjects. And for real society, there could be

" none between such as had no other sense than that of private

" good.

*' Our poet, therefore, seems not so immoderate in his cen-

** sure ; if we consider it is the heart, rather than the head, he

*^ takes to task : when reflecting on a court-education, he

" thinks it unapt to raise any affection towards a country ; and

*' looks upon young Princes and Lords as the young masters of

'' the world; who, being indulged in all their passions, and train-

" ed up in all manner of licentiousness, have that thorough con-

" tempt and disregard of Mankind, which Mankind in a man-

" ner deserves, where arbitrary power is permitted, and a ty-

" ranny adored."

While I entirely agree with the general scope of these ob-

servations, I am inclined to think, that the sensus communis of

Juvenal might be still more precisely rendered by symjoathy ;

understanding this word (in the appropriate acceptation an-

nexed to it by Mr Smith) as synonymous with that fellow-feel-

ing which disposes a man, in the discliarge of his social duties,

to place himself in the situation of others, and to regulate his

conduct accordingly. Upon this supposition, the reflection in

question coincides nearly with one of Mr Smith's own maxims,

that " the great vever look upon their inferiors as their fellow-

NOTES AND ILLUSTRATIONS. 53$

" creatures ;" *—a maxim which, akhough sufficiently founded

in fact to justify the sarcasm of the satirical poet, must (it is

to be hoped for the honour of human nature) be understood

with considerable limitations, when stated as a correct enuncia-

tion of philosophical truth.

It yet remains for me to take some notice of the sensus com-

7)iunis of the schoolmen ; an expression which is perfectly sy-

nonymous with the word conception, as defined in the first vo-

lume of this work. It denotes the power whereby the mind is

enabled to represent to itself any absent object of perception,

or any sensation which it has formerly experienced. Its seat

was supposed to be that part of tlie brain (hence called the

sensorium, or the sensorium commune) where the nerves from

all the organs of perception terminate. Of the peculiar func-

tion allotted to it in the scale of our intellectual faculties, the

following account is given by Hobbes :" Some say the senses

" receive the species of things, and deliver them to the Com-" mon Sense ; and the Common Sense delivers them over to

'* the Fancy ; and the Fancy to the Memory, and the Memory" to the Judgment ;—like handing of things from one to ano-

" ther, with many words making nothing understood.''

—

OfMan, Part I. Chap. 2.

Sir John Davis, in his poem ca the Immortality of the Soul

(published in the reign of Queen Elizabeth), gives the name of

common sense to the power of imagination (see Sections XIX.

and XX.) ; and the very same phraseology occurs, at a later

period, in the Philosophy of Descartes : (see, in particular, his

Second Meditation, where he uses Sensus Communis as syno-

nymous with Potentia Imaginatrix). Both of these writers, as

appears evidently from the context, understand by Imagina-

tion what I have called Conception. To the power yioxv denot-

ed by the word Imagination, Sir John Davis gives the name of

Fantasy.—Gassendi seems disposed to consider this use of the

phrase Sensus Communis as an innovation of Descartes, (sec

his Objections to Descartes' Second Meditatiori, § 6.), but it

had been previously adopted by various ptiilosophical writers

;

* Theory of Moral Sentimenls, Vol. I. p. 13(5, 6th edit.

6S6 NOTES AND ILLUSTRATIONS.

and, in the English schools, was at that time familiar to every

ear.

The singular variety of acceptations of which this phrase is

susceptible, and the figure which, on different occasions, it has

made in the history of philosophy, will, I trust, furnish a suffi-

cient apology for the length as well as for the miscellaneous na-

ture of the foregoing remarks.*

Note (E.) p. 105.

The Arithmetical Prodigy, alluded to in the text, is an Amerrican boy (still, I believe, in London), of whose astonishing

powers in performing, by a mental process, hitherto unexplain-

ed, the most difficult numerical operations, some accounts have

lately appeared in various literary Journals. When the sheet

containing the reference to this Note was thrown off, I enter-

tained the hope of having an opportunity, before reaching the

end of the volume, to ascertain, by personal observation, some

particulars with respect to him, which I thought might throw

light on my conclusions concerning the faculty of Attention, in

the former volume of this work. In this expectation, however,

I have been disappointed ; and have, therefore, only to apolo-

gize for having inadvertently excited a curiosity which I am at

present unable to gratify.

[Since the first edition of this volume was published, I have

seen the boy here alluded to ; but for too short a time, and un-

der too unfavourable circumstances, to be able to form any sa-

tisfactory conclusions concerning the nature of his arithmetical

* It has been observed to me very lately by a learned and ingenious

friend, that in one of the phrases which I have proposed to substitute for

the common sense of Butfier and Keid, I have been anticipated, two hundred

yeais ajô, by Sir Walter Raleigh. " Where natural reason hath built any

*' tiling so strong against itself, as the same reason can hardly assail it, much" less batter it down ; the same, in every question of nature, and infinite

" power, may be approved for a fundamental law of human knowledge."

(Preface to Raleigh's History of the World.) The coincidence, in point of

expression, is not a little curious; but is mudi less wonderful than the coin-

cidence of the thought with the soundest logical conclusions of lire eighteenth

century.—The very eloquent and philosopliical passage which immediately

iîiows the above sentence is not less worthy of attention.

NOTES AND ILLUSTRATIONS. 53?

processes. Whatever opinion may be entertained on thii*

point, every person who has witnessed his public exhibitions

must allow, that his powers of Memory and of concentrated

Attention, when contrasted with his very tender years, and with

the constitutional playfulness of his disposition, entitle him to

a conspicuous place among the rare phenomena of the intellec-

tual world. Nor can I forbear to add, that the general charac-

ter of his oivn mind seems to be simple, amiable, and interest-

ing. When farther advanced in life, he may probably have it

in his power to communicate some curious information with

respect to the origin and history of his peculiar intellectual ha-

bits. In the mean time, I nmst decline, for obvious reasons, t<*

say any thing farther on the subject.]

Note (F.) p. 172.

Ec TSiToig 7} leoT'/jg kvorrig. " In mathematical quantities, equa-

*' lity is identity."

—

Arist. Met. x. c. 3.

This passage has furnished to Dr Gillies (when treating of

the theory of syllogisms) the subject of the following comment,

in which, if I do not greatly deceive myself, he has proceeded

upon a total misapprehension of the scope of the original : "In" mathematical quantities," Aristotle says, that " equality is

" sameness," because 6 Xoyo; 6 rvig 'ôojrr,; xsiag h; kjti. " The" definition of any particular object denoted by the one is pre-

" cisely the same with the definition of any particular object

*' denoted by the other.''

—

Gillies s Aristotle, Vol. I. p. 87.

In order to enable my readers to form a judgment of the

correctness of this paraphrase, I must quote Aristotle's words,

according to his own arrangement, which, in this instance, hap-

pens to be directly contrary to that adopted by his interpreter.

Er/ 6i av 6 Xoyog 6 r'/jg •Tgwr'/^g nffiag hg r,, oiov di isai yâiiihai suinai

di aurai, x\ ra iGa)Cf

7a iGoyuvia nrsayojîa, zai roi ctas/w. a/.X' £v

ruToig 7) laoT'/ig svoTT^g. The first clause of this passage is, from

its conciseness, obscure ; but Aristotle's meaning, on the

whole, seems to be this :—" That all those magnitudes which

" bear the same ratio to the same magnitude, though in fact

" they may form a multitude, yet, in a scientific view, they

^* may be regarded as one ; the mathematical notion of equali-

538 NOTES AND ILLUSTRATIONS,

" ty being ultimately resolvable into that of" unity or iden-

" tity." * It was probably to obviate any difficulty that might

have been suggested by diversities ofjigio'c, that Aristotle has

confined his examples to equal straight lines, and to such

quadrangles as are not only equal but similar.

Let us now consider the paraphrase of Dr Gillies. " In

'* mathematical quantities, equality is sameness, because the

" definition of any particular object denoted by the one, is

" precisely the same with the definition of any particular ob-

" ject denoted by the other.'' Are we to understand by this,

that " to all things which are equal the same definition is ap-

" plicable ;" or conversely, that " all things to which the same

" definition is applicable are equal f" On the former suppo-

sition, it would iollow, that the same definition is applicable

to a circle, and to a triangle having its base equal to the cir-

cumference, and its altitude to the radius. On the latter, that

all circles are of the same magnitude ; all squares, and all

equilateral triangles.—There is, indeed, one sense wherein

those geometrical figures which are called by the same name

(all circles, for example) may be identified in the mind of

the logician ; inasmuch as any theorem v, Iiich is proved of one,

must equally hold true of all the rest ; and tlie reason of this

is assigned, with tolerable correctness, in the last clause of the

sentence quoted from Dr Gillies. But how this reason bears

on the question with respect to the convertibility of the terms

equality and sajneness, I am at a loss to conjecture.

Note (G.)p.2l6.

In an Essay on Quantity (by Dr Reid), published in the

Transactions of the Royal Society of London, for the year

1748, mathematics is very correctly defined to be " the doc-

" trine of measvire."—" The object of this science," the au-

thor observes, " is commonly said to be quantify; in which

" case, quantity ought to be defined, zvhut may be measured.

*' Those who have defined quantity to be whatever is capable

*' of more or less, have given too wide a notion of it, which

* Tct TJOC to etUTi TO/ UUTOV l)(^0V7A KO'ÔY, t7U ItKKHKOt: SfTi*

—

EUC.

F.lem, Lib. V. Piop. ix.


** has led some persons to apply mathematical reasoning to

" subjects that do not admit of it." * The appropriate objects

of this science are therefore such things alone as admit not

only of being increased and diminished, but of being multi-

plied and divided. In other ^'ords, the common quality which

characterises all of them is their mensurability.

In the same Essay, Dr Reid has illustrated, with much in-

genuity, a distinction (hinted at by Aristotle f) of quantity

into proper and improper. " I call that," says he, " proper

" quantity, which is measured by its own kind ; or which, of

*' its own nature, is capable of being doubled or trebled, with-

" out taking in any quantity of a different kind as a measure

" of it. Thus a line is measured by known lines, as inches,

" feet, or miles ; and the length of a foot being known, there

" can be no question about the length of two feet, or of any

" part or multiple of a foot. This known length, by being

" multiplied or divided, is sufficient to give us a distinct idea

" of any length whatsoever.

" Improper quantity is that which cannot be measured by" its 'own kind, but to which we assign a measure in some pro-

" per quantity that is related to it. Thus velocity of motion,

" when we consider it by itself, cannot be measured. We" may perceive one body to move faster, another slower, but

" we can perceive no proportion or ratio between their velo-

" cities, without taking in some quantity of another kind to

" measure them by. Having therefore observed, that by a.

" greater velocity, a greater space is passed over in the same

" time, by a less velocity a less space, and by an equal velo-

" city an equal space ; we hence learn to measure velocity by" the space passed over in a given time, and to reckon it to be

" in exact proportion to that ; and having once assigned this

* In this remark, Dr Reid, as appears from the title of his paper, had an

eye to the abuse of mathematical language by Dr Hutcheson, who had re-

cently catried it so far as to exhibit algebrairal formulas for ascertaininj;

the moral merit or demerit of particular actions. (Sue his Inquiry into the

Original of our Ideas of Beauty and Virtue.)

t Ki/giccc tfs rtofl-st tauTOL KiyiTcu nova, tn Si AXXct TraVTct itHTtt ffUfX'

ySt.fixKof «{ Ttturx yug aTto^hiJrovTtSi >^ t« a\Mt OosrsB Kiya[jkiu—Arist.

C'ateg. cap. vi. 17.


*' measure to it, we can then, and not till then, conceive one

" velocity exactly double, or triple, or in any proportion to

* another. We can then introduce it into mathematical rea-

<* soning, without danger of error or confusion ; and may use

*' it as a measure of other improper quantities.

" All the proper quantities we know may, I think, be re-

*' duced to these four : extension, duration, number, and pro-

** portion.

" Velocity, the quantity of motion, density, elasticity, the

*' vis insita and impressa, the various kinds of centripetal forces,

*' and the different orders of fluxions, are all improper quanti-

*' ties ; which therefore ought not to be admitted into mathe-

*' matical reasoning, without having a measure of them as-i

*' signed.

" The measure of an improper quantity ought always to be

*' included in the definition of it ; for it is the giving it a mea-

** sure that makes it a proper subject of mathematical rcason-

" ing. If all mathematicians had considered this as carefully

" as Sir Isaac Newton has done, some trouble had been saved

*' both to themselves and their readers. Tliat great man,

" whose clear and comprehensive understanding appears even

*' in his definitions, having frequent occasion to treat of such

*' improper quantities, never fails to define them, so as to give

*' a measure of them, either in proper quantities, or such a*

*' had a known measure. See the definitions prefixed to his

<' Principia."

With these important remarks I entirely agree, excepting

only the enumeration here given of the different kinds of pro-

per quantity, which is liable to obvious and insurmountable

objections. It appears to me that, according to Reid's own

definition, extension is the only proper quantity within the

circle of our knowledge. Duration is manifestly not mea-

sured by duration, in the same maimer as a line is measured

by a line ; but by some regulated motion, as that of the

hand of a clock, or of the shadow on a sun-dial. In this re-

spect it is precisely on the same footing with velocities and

forces, all of them being measured, in the last result, by ex-

tension. As to number and proportion, it might be e&sily

NOTES AND ILLUSTRATIONS. 54l

shewn, that neither of them fall under the definition of quan-

tity, in any sense of that word. In proof of this assertion

(which may, at first sight, seem somewhat paradoxical), I have

only to refer to the mathematical lectures of Dr Ba,rrow, and

to some very judicious observations introduced by Dr Clarke

in his controversy with Leibnitz. It is remarkable, that, at

the period when this essay was written, Dr Reid should have

been unacquainted with the speculations of these illustrious

men on the same subject ; but this detracts little from the me-

rits of his memoir, which rest chiefly on the sti'ictures it con-

tains on the controversy between the Newtonians and Leib-

nitzians concerning the measure of forces.

Note (H.) p. 218.

The following view of the relation between the theorems of

pure geometry and their practical applications strikes me as

singularly happy and luminous ; more especially the ingenious

illustration borrowed from the science of geometry itself:

*' Les verites que la geometrie demontre sur I'etendue, sonf

*' des verites purement hypothetiques. Ces verites cependant

** n'en sont pas moins utiles, eu egard aux consequences pra-

" tiques qui en resultent. Jl est aise de le faire sentir par une

" comparaison tiree de la geometrie meme. On connoit dans

*' cette science des lignes courbes qui doivent s'approcher con-

" tinuellement d'une ligne droite, sans la rencontrer jamais, et

** qui neanmoins, etant tracees sur le papier, se confondent

' sensiblement avec cette ligne droite au bout d'un assez petit

•* espace. II en est de meme des propositions de geometric

;

*' elles sont la limite intellectuelle des verites physiques, le terme

" dont celles-ci peuvent approcher aussi pres qu'on le desire,

** sans jamais y arn\'er exactement. Mais si les thcoremes

*' mathematiques n'ont pas rigoureusement lieu dans la nature,

<' ils servent du moins a resoudre, avec une precision suffisante

•' pour la pratique, les difFerentes questions qu'on pent se pro-

" poser sur I'etendue. Dans I'univers il n'y a point de cercle

" parfait ; mais plus un cercle approchera de I'etre, plus il ap-

" prochera des proprietes rigoureuses du cercle parfait que la

*' geometrie demontre ; et il peut en approcher a un degre suf-


" fisant pour iiotre usage. II en est de meme des autres figures

" dont la geometrie detaille les proprietes. Pour demontrer

" en toute rigueur, les verites relatives a la figure des corps,

" on est oblige de supposer dans cette figure une perfection ar-

" bitraire qui n'y sauroit etre. En efFet, si le cercle, par ex-

<* emple, n'est pas suppose rigoureux, il fiiudra autant de theo-

" remes difi"erens sur le cercle qu'on imaginera de figures dif-

" ferentes plus ou moins approchantes du cercle parfait ; et

" ces figures elles-memes pourront encore etre absolument hy-

" pothetiques, et n'avoir point de modele existant dans la na-

" ture. Les lignes qu'on considere dans la geometrie usuelle,

*' ne sont ni parfaitement droites, ni parfaitement courbes ; les

" surfaces ne sont ni parfaitement planes, ni parfaitement cur-

" vilignes ; mais il est necessaire de les supposer telles, pour

" arriver a des verites fixes et determinees, dont on puissefaire

" ensuite I'application plus ou moins exacte aux lignes et aux

" surfaces physiques."—D'Alembert, Eltmens de Philosophie,

Article Geometrie,

Note (I.) p. 236".

From some expressions in this quotation, it would seem that

the writer considered it as now established by mathematical

demonstration, not only that a provision is made for maintain-

ing the order and the stability of the solar system ; but that,

after certain periods, all the changes arising from the mutual

actions of the planets, begin again to be repeated over in an

invariable and GievndX round

;

—or leather, that all this is the

result of the necessary properties of matter and of motion. So

completely unfounded is this assumption, in point of fact, that

the astronomical discovery in question affords not the slightest

analogical presumption in favour of a moral cycle ;—even on

the supposition, that the actions of the human race, and the

motions of the globe which they inhabit, were both equally sub-

jected to the laws of mechanism.

I shall avail myself of this opportunity to remark further,

that, notwithstanding the lustre thrown by the result of La

Grange's investigations on the metaphysical reasoning of Leib-

nitz against the manus emendatrix of Newton,—this reasoning.

JJOTES AND ILLUSTRATIONS. 54>S

wlien we consider the vagueness of the abstract principles on

which it rests, can be regarded in no other light than as a for-

tunate conjecture on a subject where he had neither experience

nor analogy for a sjuide. The following arpument is not ill-

Stated by Voltaire ; and, in my opinion, is more plausible than

any thing alleged a priori, on the other side of the question,

by Leibnitz :" II est trop clair par I'experience que Dieu a

" fait des machines pour etre detruites. Nous sommes I'ouv-

'^' rage de sa sagesse ; et nous perissons. Pourquoi n'en se-

'' roit-il pas de meme du monde ? Leibnitz veut que ce monde*' soit parfait; mais si Dieu ne I'a forme que pour durer ua" certain terns, sa perfection consiste alors a ne durer que

*' jusqu'a i'instant fixe pour sa dissolution."

—

Voltaire s Ac-

count of Newton s PliiUysophy,

For some excellent observations on these opposite conjec-

tures of Leibnitz and of Newton, see Edinburgh Review,

Vol. XIV. pp. 80, SI.

The quotation which gave occasion to the foregoing stric-

tures induces me to add, before concluding this Note, that

when we speak of La Grange's Demonstration of the Stability

of the Solar System, it is by no means to be understood that

he has proved, by mathematical reasoning, that this system

never mil, nor ever can, come to an end. The amount of his

truly sublime discover}' is, that the system does not, as Newton

imagined, contain v.ithin itself, like the workmanship of mortal

hands, the elements of its own decay ; and that, therefore, its

final dissolution is to be looked for, not from the operation of

physical causes subjected to the calculations of astronomers,

but from the v»'ill of that Almighty Being, by v/hose Jlat it

was at first called into existence. That this stability is a ?2e-

cessary consequence of the general laws by which we find the

system to be governed, may, indeed, be assumed as a demon-

strated proposition ; but it must always be remembered, that

this necessity is oidij hypothetical or conditional, being itself de-

pendent on the continuance of laws, which may at pleasure be

altered or suspended.

The whole of the argument in the text, on the nermanence

or stability of the order of nature, is manifestly to be under-

544 NOTES AND ILLUSTRATIONS*

stood with similar restrictions. It relates, not to necessary bul

to probable truths ; not to conclusions syllogistically deduced

from abstract principles, but X,ofuture, contingencies^ which we

are determined to expect by a fundamental Law of Belief,

adapted to the present scene of our speculations and actions.

Note (K.) p. 242.

*' The power of designating an individual object by an ap-

*' propriate articulation, is a necessary step in the formation of

*' language, but very far removed indeed from its consumma-'' tion. Without the use of general signs, the speech of man*' would differ little from that of brutes ; and the transition to

" the general term from the name of the individual, is a diffi-

*' culty which remains still to be surmounted. Condillac, in-

'* deed, proposes to shew how this transition may be made in

" the natural course of things. ' Un enfant appelle du nom" d'arbre le premier arbre que nous lui montrons. Un second

" arbre qu'il voit ensuite lui rappelle la meme idee ; il lui

" donne le meme nom ; de meme a un troisieme, a un qua-

" trieme, et voila le mot d'arhre, donne d'abord a un individu,

" qui devient pour lui un nom de classe on de genre, une idee

" abstraite qui comprend tous les arbres en general.' In like

*' manner, Mr Adam Smith, in his Dissertation on the Origin

" ofLanguages^ and Mr Dugald Stewart, in his Elements of the

" Philosophy/ of the Human Mind, endeavour to explain this

*' process, by representing those words which were originally

" used as the proper names of individuals, to be successively

" transferred to other individuals, until at length each of thera

*' became insensibly the common name of a multitude. This,

" however, is more ingenious than solid. The name given to

" an individual, being intended exclusively to designate that

" individual, it is a direct subversion of its very nature and de-

*' sign to apply it to any other Individual, known to be different

" from the former. The child, it is true, may give the name** o?father to an individual like to the person it has been

** taught to call by that name : but this is from mistake, not

*' from design ; from a confusion of the two as the same per-

" son, and not from a perception of resemblance between them

NOTES AND ILLUSTRATIONS. 545" whilst known to be difFerent. In truth, they whose thoughts

*< are occupied solely about individual objects, must be the

" more careful to distinguish them from each other; and, ac-

" cordiiigly, the child will most peremptorily retract the ap-

*' pellation oifather, so soon as the distinctness is observed.*

*' The object with those whose terms or signs refer only to in-

" dividuals, must naturally be to take care, that every such

" term or sign shall be applied to its appropriate individual,

" and to none else. Resemblance can produce no other ef-

" feet, than to enforce a greater caution in the application of

" the particular names, and therefore has no natural tendency

" to lead the mind to the use of general terms."

—

Discourses

and Dissertations on the Scriptural Doctrines of Atonement

and Sacrifice. By William Magee, D. D, Senior Fellow of

Trinity College, and Professor of Mathematics in the Uni-

versity of Dublin. Vol. II. pp. 63, 64-. 3d edit.

The observations in pp. 242, 243, &c. of this volume (to

which I must request the attention of my readers before they

proceed to the following remarks), appear to me to weaken con-

siderably the force of this reasoning, as far as it applies to the

substance of the theory in question. With respect to MrSmith's illustration, drawn from the accident of a child's calling

a stranger by the name oifather, I readily acknowledge that

it was unluckily chosen ; and I perfectly assent to the stric-

tures bestowed on it by Dr Magee. In consequence of the

habitual intercourse which this domestic relation naturally

keeps up between the parties, the mistake of the child (as DrMagee very properly calls it) must, of course, be immediately

corrected ; and, therefore, the example is of no use whatever in

confirming the conclusion it is brought to support. It is to be

regretted that, upon this occasion, Mr Smith should not only

have appealed to a period of infancy, when the notions of simi-

* Tliese remarks have a paiticiilar reference to the following sentence

in Mr Smith's Dissertation : " A child that is just learning to speak calls

«« every peison who comes to the iiouse its papa or its mama ; and thus be-

" stows upon the whole species tliose names wiiich it had been taught to

" apply to two individuals."

VOL. II. M m

64i6 NOTES AND ILLUSTRATIONS.

larity and of identity cannot fail to be sometimes one and the

same ; but should have assumed, as a general fact, an acciden-

tal occurrence, which, if it ever has happened, may be justly

regarded as an exception to the usual history of the species.

While yet on the breast, a child is able to distinguish, with the

utmost quickness and accuracy, between the face of an ac-

quaintance and that of a stranger ; and, when it is so far ad-

vanced as to begin to utter articulate sounds, any tendency

to transfer or to generahze the words mother or nurse seems

scarcely conceivable. We are apt to suppose that the first at-

tempts towards speech are coeval with the study of language

;

whereas the fact manifestly is, that these attempts are only the

consequences of the progress previously and silently made in

the interpretation of words. Long before this time, many of

the logical difficulties, which appear so puzzling to the specula-

tive grammarian, have been completely surmounted. *

But although this particular example has been ill chosen, it

does not therefore follow that the author's theory is altogether

unfounded, ^^'hoever has paid any attention to the pheno-

mena of the infant mind, must be satisfied of its strong bias, in

the first developement of the intellectual powers, to apply to

similar objects a common name, without ever thinking of con-

founding them together.—Nor does this hold merely with re-

spect to similar objects : it holds also (and at a surprisingly

early period of life) with respect to similar relations. A child

who has been accustomed to the constant attentions and ca-

* The gtmral fact with respect to children, assumed by Mr Smith in the

foregoing note, is stated slill more strongly by Aristotle. Both of these

pliilosopliers liave, I suspect, trtistcd more, in this instance, to theory than

to observation. Ka/ rt- Tntiîu to /msv ^âiTov wgoiraôgst/s/ TTdLvrat tsc

T6gov. " Ac piien quoqiie piinnVn oinnes viros appellant paties, et omnes

" ninlieres, nialres: postea veio discernunt horum utrumquf."

—

Arist. Nat.

Aiisc. Lib. I. Cup. i.

Tills passage (wliich I do not recoUrct lo have seen quoted l)y any former

writi:)) does honour to Aiistoth^'s acuteness. The fact, indeed, asserted in

it, is more than questionable ; but, admitting the fact to be true, it must be

owned that Aiistotle has viewed it in a justcr light than Mr Smith ;—not as

an instance of ariv disposition to generalize proper names, but merely of

imperfect and undistinguishiug perception.

6


vesses of its mother, when it sees another child in the arms of

its nurse, will naturally and infallibly call the nurse the child's

mother. In this instance, as in numberless others, its error

arises from generalizing too hastily ;—the distinction between

the meanings of the two relative words IVIother and Nurse be-

ing too complex to be comprehended, till the power of obser-

vation begins to be exercised with some degree of attention

and accuracy. This disposition, however, to transfer names

from one thing to another, the diversity of which is obvious

even to sense, certainly affords no inconsiderable an argument

in favour of the opinion disputed by Dr Magee.

It is, indeed, wonderful, how readily children transfer or ge-

neralize the name of the maternal relation [that which of all

others must necessarily impress their minds most strongly) not

only in the case of their own species, but of the lower animals

;

applying, with little or no aid from instruction, the word mo-

ther to the hen, the sheep, or the cow, whom they see employ-

ed in nurturing and cherishing their young.

To myself, I own, it appears, that the theory of Condillac

and Smith on this point is confirmed by every thing I have

been able to observe of children. Even generic terms will be

found, on examination, if I be not much deceived, to be origi-

nally understood by them merely as proper iiames ; insomuch,

that the notions annexed by an infant to the v/ords denoting

the different articles of its nursery-furniture, or the little toys

collected for its amusement, are, in its conceptions, as indivi-

dually and exclusively appropriated, as the names of its father,

mother, or nurse. If this observation be well-founded, the

same gradual conversion of proper names into appellatives,

which Mr Smith supposes to have taken place in the forniiition

of a language, is exemplified in the history of every infant

while learning to interpret its mother-tongue. The case is

nearly the same with the peasant, who has never seen but one

town, one lake, or one river. All of these appellatives are to

his ear precisely equivalent to so many proper names.

" Quo te, Mceri, pedes? An, quo via ducif, in Urbem?"

That resemblance is one of our most powerful associating

principles will not be disputed ; and that, even in the maturity


of our reason, we have a natural disposition to generalize the

meaning of signs, in consequence of apprehended similarities,

both of things and of relations, is equally certain. Why then

should it be apprehended, that there is any peculiar mystery

connected with this step in the commencement of the progress,

when it seems to admit of an explanation so satisfactory, from

a law of the human mind, exemplified daily in facts falling

within the circle of our own experience ?

Note (L.) p. 270.

" Aristotle's rules are illustrated, or rather, in my opinion,

" purposely darkened, by putting letters of the alphabet for the

" several terms.''

—

Reid's Analysis of Aristotle s Logic.

On this remark the following criticism has been made by DrGillies

:

" In the first Analytics, Aristotle shews, what is that ar-

" rangement of terms in each proposition, and that arrange-

" ment of propositions in each syllogism, which constitutes a

" necessary connection between the premises and the conclu-

" sion. When this connection takes place, the syllogism is

" perfect in point of form ; and when the form is perfect, the

" conclusion ^necessarily follows from the premises, whatever

" be the signification of the terms of which they are composed.

" These terms, therefore, he commonly expresses by the let-

" ters of the alphabet, for the purpose of shewing that our as-

" sent to the conclusion results, not from comparing the things

" signified, but merely from considering the relation which

" the signs (whether words or letters) bear to each other.

" Those, therefore, totally misconceive the meaning of Ari-

" stotle's logic, who think that, by employing letters instead of

" words, he has darkened the subject ; since the more abstract

" and general his signs are, they must be the better adapted

'* to shew, that the inference results from considering them

" alone, without at all regarding the things which they sig-

" nify." *

• Analysis of Aristotle's Speculative Works, Sue. by Dr Gillies, Vol. I.

p. 89, 2d edit.

From a iiole at the foot of the page ii appears, tliat the remarks jiisl

quoted from Reid gave occasion to the above strictures.


With the doctrine stated in the beginning of this extract I

entirely agree. It coincides, indeed, remarkably with a pas-

sage in the former volume of this work, where I have shewn,

at some length, that our assent to the conclusion of a legiti-

mate syllogism results, not from comparing the things signified,

but merely from considering the relations of the signs ; and,

consequently, that letters of the alphabet might be substituted

instead of verbal terms, without impairing the force of the ar-

gument. The observation appears to myself of considerable

importance, when connected with the fundamental question

there discussed, concerning the use of language as an instru-

ment of thoifght ; but, I own, I am at a loss to conceive how

it should have been supposed to bear on the present subject.

The only point at issue between Dr Gillies and Dr Reid is,

whether the use of letters instead of words be, or be not, a

useful expedient for facilitating the study of logic ; and upon

this, I apprehend, there can scarcely exist a diversity of opi-

nion. No instance, I will venture to affirm, ever occurred of any

hesitation in the mind of the merest novice about the conclu-

siveness of a legitimate syllogism, when illustrated by an ex-

ample ; but how difficult to explain to a person altogether un-

accustomed to scholastic abstractions, the import and cogency

of those symbolical demonstrations by which Aristotle has at-

tempted to fortify the syllogistic theory !

The partiîty of Dr Gillies for this technical device has pro-

bably arisen, in part, from his supposing it to bear a much closer

analogy than it does, in fact, to the algebraical art. Another

very learned writer has proceeded on the same idea, when he

observes, that *' it should recommend the study of logic to ma-

" thematicians, that, in order to make his demonstrations uni-

" versal, Aristotle uses letters as universal characters, stand-

*' ing for all kinds of terms or propositions.'' * It would be an

idle waste of words to shew how very slight this analogy is,

and how totally inapplicable to the question before us ;

—

amounting to little more than this, that, in both cases, the al-

phabet happens to be employed as a substitute for commonlanguage. An analogy, much more in point, may be traced in

* Ancient Metaphysics, Vol. IIL p. 51 of the Preface.


the practice of designating by letters the different parties in 3

hypothetical law-suit ;—a practice attended with no inconveni-

ence, where these symbols only supply the place of proper

names ; but which would at once convert the simplest case in-

to an senigma, if they were to be employed (as they are by

Aristotle) to denote, not merely individual existences, but the

relations of general ideas.

While Dr Gillies has thus exerted his ingenuity in defend-

ing the use made by Aristotle of letters instead of words, it is

to be regretted, that he has said nothing about the motives

which induced that philosopher, in disproving the illegitimate

modes, to content himself with general references to such

words as honnm. habitus, prudentia, upon which the student is

left to his own judgment, in ringing the various changes ne-

cessary tor the illustration of the theory. A more effectual

contrivance could not easily have been thought of, for perplex-

ing a subject, level, in itself, to the meanest capacity. In this

respect, it answers the intended purpose still better than his

alphabeticalyo;-»?»te.

Note (M.) p. 309.

As instances of what are called by logiciansj^Z/rtc/^ in die-

tione, a modern writer mentions the mistakes which may arise

from confounding " liber Bacchus, et liber a servitute ; liber

" codex, et liber cortex ; crevi a cerno, et crevi a cresco ; in-

"fractus participium ab injringo, et iiifractus compositum ab

" in et Jradus, sensu plane contrario." He mentions also the

danger of confounding the literal with the figurative sense of

a word, as ridpcs when applied to a quadruped, and to a man

noted for cunning.—" Sicsiquis arguat," he adds lor the sake

of illustration, " stellam latrare, quia stella qua;dam Cnnis di-

" citur, facile respondebitur captioso argumento, distinguendo

" varios sensus ejusdem vocis, indeque ostendendo syllogismi

" quatuor terminos (si sensum spectes) ubi tres saltern sono

" comparent."

To exemplify the fallacia accentus, the same writer warns

us against confounding hortiis and ortits ; liara and nra ; ma-

lum adjectivum, and malum pro porno ; cerxms and servus ;

concilium and consilium, &c. &c. The remedy against such


fallacies, he gravely tolls us, is to distinguisli the words thus

identified, so as to shew that the syllogism consists ol' more

than three terms. " Solvuntur distinguendo ea qua; cont'un-

" duntur, indeque monstrando piuralitatem terminoruni." He

acknowledges, however, that fallacies of this sort are not iiKC-

ly to impose on a skilful logician. " Sed crassiores sunt ha;

" fallacias quam ut perito imponant."

I have purposely quoted these remarks, not from a mere

schoolman, but from an author justly distinguished both by

science and learning, Dr Wailis of Oxford. They are taken,

too, from a treatise written with the express view of adaptaig

the logic commonly taught in our universities to the ordinary

business of life ; having a formal dedication prefixed to it to

the Royal Society of London, then recently instituted. The

subject is the same with that of the third Book of Locke's Es-

say, relating to the cfZiwê o/toorrf^,- and the interval between

the two publications was only two years. Yet how immense

the space by which they are separated in the history of the

Human Mind

!

The concluding paragraph, however, of this very puerile

chapter on sophisms, bears marks of a mind fitted for higher

undertakings. I cannot deny myself the pleasure of transcrib-

ing it, and of pointing it out to those who may hereafter spe-

culate upon the theory of wit, as not unworthy of their atten-

tion.

" Literimhic raonendum duco ; quod hxfallacice, utcunque

" justam argumenti vim non habeant, apprime tamen com-

" modae sunt ad id omne quod ingeniosum vulgo dicimus : Ut" sunt joci, facetia;, dicteria, scommata, sarcasmi, retorsiones

" lepidse (rvit, raillerij, repartee). Quippe hoc omne fundari

" solet in hujusmodi fallaciarum aliqua. Nonnunquam allusio

" fit ad verborum sonos ; nunc ad ambiguam vocum significa-

' tio nem ; nunc ad dubiam syntaxin ; nunc proverbialiter dici

" solita accommodantur sensu proprio, aut vice versa : nunc

" aliud aperte dicitur, aliud clam insinuatur ; saltern oblique

" insinuatur, quod non erat directo dicendum ; nunc verba

*' contrario sensu captantur, et retorquentur ; nunc verisimile

" insinuatur ut verum, saltern ut suspectum ; nunc dc uno di-


" citur, quod mutato nomine, de alio intellectual vellent ; nune

" ironice laudando vituperant ; nunc objecta spicula, respon-

" dendo declinantur, aut etiam (obliquata) alio diriguntur,

" forte sic ut auctorem feriant ; et fere semper ex ambiguo** luditur. Quae quidem fallaciarum formulae, si frigidae sint

" crassaeque, ridentur ; si subtiliores arrident ; si acutae, titil-

" lant ; si aculeatae, pungunt."

Note (N.) p. 333.

In the first volume of these Elements, I have endeavoured

to trace the origin of that bias of tlie imagination, which has led

men, in all ages of the world, to consider physical causes and ef-

fects as a series of successive events necessarily connected to-

gether like the links of a metallic chain. (See Chap. i. Sect. 2.)

So very strong is this bias, that, even in the present times, some

of the most sagacious and cautious of Bacon's followers occa-

sionally shew a disposition to relapse into the figurative lan-

guage of the multitude. " The chain of natural causes,'' says

Dr Reid, " has, not unfitly, been compared to a chain hanging

*' down from heaven : A link that is discovered supports the

" links below it, but it must itself be supported ; and that

" which supports it must be supported, until we come to the

" first link, which is supported by the throne of the Almighty."

—Essays on the Intellectual Poivers, p. 115. 4to ed.— It is

difficult to reconcile the approbation here bestowed on the

above similitude, with the excellent and profound remarks on

the relation of cause and effect, which occur in other parts of

Dr Reid's works.—See Essays on the Active Poivers, p. 44,

and pp. 286, 287, 288. 4to ed.

Mr Maclaurin, in the concluding chapter of his Account of

Newton's Discoveries, has still more explicitly lent the sanc-

tion of his name to this idea of a chain of second causes. " As

" we cannot but conce ve the universe as depending on the

" first cause and chief mover, whom it would be absurd, not

" to say impious, to exclude from acting in it ; so we have

" some hints of the manner in which he operates in nature, from

" the laws which we find established in it. Though he is the

" source of all efficacy, yet we find that place is left for second


" causes, to act in subordination to him ; and mechanism has its

** share in carrying on the great scheme of nature. The esta-

** bhshing the equality of action and reaction, even in those

** powers which seem to surpass mechanism, and to be more

" immediately derived from him, seems to be an indication

*' that those powers, while they derive their efficacy from him,

** are, however, in a certain degree, circumscribed and regu-

" lated in their operations by mechanical principles ; and that

** they are not to be considered as mere immediate volitions of*' his (as they are often represented), but rather as instru-

" ments made by him, to perform the purposes for which he

" intended them. If, for example, the most noble phenomena

" in nature be produced by a rare elastic cetherial medium, as

" Sir Isaac Newton conjectured, the whole efficacy of this

*' medium must be resolved into his power and will who is the

•' supreme cause. This, however, does not hinder, but that

*' the same medium may be subject to the like laws as other

" elastic fluids, in its actions and vibrations ; and that, if its

" nature were better known to us, we might make curious and

" useful discoveries concerning its effects from these laws. It

" is easy to see, that this conjecture no way derogates from the

" government and influences of the Deity ; while it leaves us at

" liberty to pursue our inquiries concerning the nature and

" opei'ations of such a medium : Whereas they who hastily re-

" solve these powers into immediate volitions of the Supreme

" Cause, without admitting any intermediate instruments, put

" an end to our inquiries at once ; and deprive us ofwhat is prO'

" bably the most sublime part of philosophy, by representing it

" as imaginary andjictitious."

On the merits of this passage, considered in relation to the

evidences of natural religion, I do not mean to offer any re-

marks here. Some acute strictures upon it in this point of

view (but expressed with a most unbecoming and offensive pe-

tulance) may be found in the third volume of Baxter's Inquiry

into the Human Soul.—It is with the logical proposition alone,

stated in the concluding sentence, that we are concerned at

present; and this (although Baxter has passed it over without

any animadversion) appears to me highly exceptionable ; pro-

554i NOTES AND ILLUSTRATIONS,

ceeding on a very inaccurate, or rather totally erroneous con-

ception of the object and aim of physical science. From the

sequel of the section to which this note refers (particularly

from pages 338, 339, 340, 341 ), I trust it will appear, that,

supposing all the phenomena of the universe to be produced

by the immediate volitions of the Supreme Cause, the business

of natural philosophers would be precisely the same as upon

the hypothesis adopted by Maclaurin ; the investigation of the

nexessary connections linking together physical causes and ef-

fects (if any such necessary connections do exist)^being con-

fessedly placed beyond the reach of our faculties ; and, of con-

sequence, our most successful researches terminating in the

discovery of some general law, or in the farther generalization

and simplification of laws already know-n. In this intellectual

process there is no more reason to apprehend that any limit is

fixed to our inquiries, than that the future progress of geome-

try should be stopped by the discovery of some one truth com-

prising the whole science in a single theorem.

Nor do I apprehend that the theory which excludes from the

universe mechanism (strictly so called) tends, in the smallest de-

gree, to detract from its beauty and grandeur; notwithstanding

the popular and much admired argument of Mr Boyle in sup-

port of this idea. "As it more recommends," he observes,

" the skill of an engineer to contrive an elaborate engine, so

" as that there need nothing to reach his ends in it, but the

" contrivance of parts void of understanding ; than if it were

" necessary that, ever and anon, a discreet servant should

" be employed to concur notably to the operations of this

" or that part, or to hinder the engine from being out of

" order: so it more sets oft" the wisdom of God, in the fa-

" brie of the universe, that he can make so vast a machine

** perform all those many things which he designed it should,

" by the mere contrivance of brute matter, managed by cer-

*' tarn laws of motion, and upheld by his ordinary and ge-

" neral concourse ; than if he employed, from time to time,

" an intelligent overseer to regulate and control the mo-

" tion of the parts.'' *—" What may be the opinion of

* Inquiry into the vulgar notion of Nature.


" otlicrs," says Lord Kames, after quoting the foregoing

passage), " I cannot say ; but to me this argument is perfectly

" conclusive. Considering this universe as a great machine,

" the workmanship of an intelligent cause, 1 cannot avoid

" thiuking it tiie more complete, die less mending or interpo-

" sition it requires. The perfection of every piece of work-

** manship, human and divine, consists in its answering the de-

" feigned purpose, uitliout bestowing further labour upon it."*

—To myself, I must confess, Mr Boyle's argument appears al-

together unworthy of its author. The avowed use of a machine

is to save labour ; and, therefore, the less frequently the inter-

position of the artist is necessary, the more completely does

the machine accomplish the purpose for which it was made.

These ideas surely do not apply to the works of the Almighty.

The multiplicity of his operations neither distract his attention,

nor exhaust his power ; nor can we, without an obvious incon-

sistency in the very terms of the proposition, suppose him re-

duced to the necessity of economizing, by means of mecha-

nism, the resources of Omnipotence, f

My object in these observations (I think it proper once more

to remind my readers) is not to prejudge the metaphysical

question between Maclaurin and Baxter ; but merely to esta-

blish the two following propositions. 1. That this question is

altogether foreign to the principles which form the basis of the

inductive logic ; these principles neither affirming nor denying

the existence of necessary connections between physical causes

and effects, but only asserting, that such connections, if they

do exist, are not objects of human knowledge. 2. That no

presumption in favour of their existence is afforded by MrBoyle's similitude ; the reasoning founded on the supposed

* Of tlie Laws of Motion, rublishet! in tlie First Volume of the Pbj-

sical and Literary Essays, read before the Edinburgh Plnlosopliical Society.

(1754.)

t A comparison, still more absurd tlian that of Mr Boyle, occms in the

eili Chapter of Aristotle's book De Mundo; ukerehe represents it as unbe-

connna the dignity of the Supreme Heing ettiTHpynv uTravTci,—" to put his

*' own hand to every tiling;" a supposition, aecordins;; to him, " much more

" unsuitable to the pivine majesty, than to conceive a great monarch like

f Xerxes taking upon himself the actual execution of all his own decrees.


analogy between the universe and a machine, being manifest-

ly inapplicable where the jôiver as well as the skill of the Con-

triver is admitted to be infinite.—If the remarks offered on

these points be well-founded, they may serve, at the same time,

to shew, that the attempt made in the text to illustrate some

abstract topics connected with the received Rules of Philoso-

phising was not altogether superfluous.

The metaphysical doctrine maintained by Baxter, in opposi-

tion to Maclaurin, seems to coincide nearly with Malebranche's

Theory of Occasional Cau.ses, as well as with the theology of

the old Orphic verses quoted in the 7th chapter of Aristotle's

Treatise De Mundo.—A very striking resemblance is observable

between these verses, and the Hymn to Narrayna or the Spirit

of God, translated by Sir William Jones from the writings of

ancient Hindu Poets.*

Note (O.) p. 351.

Although Dr Reid was plainly led into this train of thinking

by Mr Hume, the same doctrine, with respect to the relation

of cause and effect (considered as the object of physical

science), is to be found in many English writers of a far earlier

date. Of this assertion I have produced various proofs in myfirst volume, from Hobbes, Barrow, Berkeley, and others, to

whose speculations on this head Dr Reid does not seem to have

paid any attention. To these quotations I beg leave to add the

following, from a book, of which the third edition was publish-

ed in 1737.

" Here it is worth observing, that all the real true know-

** ledge we have of nature is entii'ely experimental ; insomuch,

•' that how strange soever the assertion seems, we may lay this

" down as the first fundamental unerring rule in physics, that

" it is not toiihin the compass of human understanding to assign

*' a fureiy speculative reasonyor any one phenomenon in nature ;

* The same opinion is explicitly avowed liyDr Clarke, a zealous partisan

of the Experimental Pliilosophy, ami one of the ablest logicians that tlie

Newtoiiiiin School has hitherto produced. " The course of nature, truly

" and properly speaking, is iiothini; but the will of God, producing certain

" effects in a continued, regular, constmit, and uniform manner."—darkens

Works, Vol. 11. p. 698, Fol. edit.

NOTES AND ILLUSTRATIONS. 5S^

" as why grass is green, or snow is white ; why fire burns, or

*' cold congeals. By a speculative reason, I mean assigning an

*' immediate efficient cause a priori, together with the manner

*< of its operation, for any effect whatsoever purely natural*

*' We find, indeed, by observation and experience, that such

" and such effects are produced ; but when v/e attempt to

" think of the reason ivhy, and the manner hoio the causes

" work those effects, then we are at a stand, and all our rea-

" soning is pi-ecarious, or at best but probable conjecture.

" If any man is surprised at this, let him instance, in some*' speculative reason he can give for any natural phenomenon

;

" and how plausible soever it appears to him at first, he will,

" upon weighing it thoroughly, find it at last resolved into no-

*' thing more than mere observation and experiment, and will

" perceive that these expressions generally used to describe

" the cause or manner of the productions of nature, do really

" signify nothing more than the effectsJ'—The Procedure,

Extents, and Limits of Huwan Understanding. Ascribed

to Dr Peter Brown, Bishop of Cork. (London, 1737, 3d ed.)

For the following very curious extracts (together with many

others of a similar import, both from English and from Foreign

writers) I am indebted to a learned correspondent, William

Dickson, LL. D., a gentleman well known by his able and me-

ritorious exertions' for the abolition of the slave-trade.

" Confidence of science is one great reason we miss it : for

*' on this account, presuming we have it everywhere, we seek

" it not where it is ; and, therefore, fall short of t!ie object of

" our inquiry. Now, to give further check to dogmatical pre-

" tensions, and to discover the vanity of assuming ignorance,

" we'll make a short inquiry, whether there be any such thing

" as science in the sense of its assertors. In their notion, then,

*' it is the kno'voledge oj' tilings in their true, immediate, necessary

" causes : Upon this I'll advance the following observations :

" 1. All knowledge of causes is deductive ; for we know" none by simple intuition, but through the mediation of their

^' effects. So that we cannot conclude any thing to be the

*' cause of another, but from its continual accompanying it

;


„ for the causality itself is insensible. But now to argue from.

" a cOTicomitancy to a causality is not infallibly conclusive ;

" yea, in this way lies notorious delusion, &c. &c. &c.

" 2. "yVê hold no demonstration in the notion of the dogma-'' tist, but where the contrary is impossible :" &c. <S:c. {Scep-

sis Scientifica : or Confess't Ignorance the Way to Science

;

in an Essay of the Vanity of Dogmatizing and Confident Opi-

nion ; with a Reply to the Exceptions of the learned Thomas

Albius.* By Joseph Glanvill, M. A. London, 1 665. Dedi-

cated to the Royal Society.)

" Causalities are first found out by concomitancy, as I inti-

" mated. And our experience of the dependence of one, and*' independence of the other, shews which is tho effect, and

" which the cause. Definitions cannot discover causalities, for

" they are formed after the causality is known. So that, in

" our author's instance, a man cannot know heat to be the

" atoms of fire, till the concoraitancy be known, and the efii-

" ciency first presumed. The question is, then, How heat is

" known to be the effect o^ fire ? Our author answers by its

*' definition. But how came it to be so defined ? The answer

'' must be, by the concomitancy and dependence, for thei'e's

"nothing else assignable." (SClR^tuum nihil est; or the

Author's Defence of the Vanity of Dogmatizing against the

Exceptions of the learned Thomas Albius, in his late SCIRI.)

London, 1665

" Inter causam proprie dictam et effectum oportet esse ne-

" cessarium nexum ; adeo ut posita actione causae sequatur

" necessai'io effectus. Cum Deus vult aliquid efficere id neces-

" sario eveniat oportet, &c. Quia autem ejusmodi nexus non

" cernitur inter causas creatas et effectus, nonnulli causas se-

" cundas, seu creatas, sua vi agere negarunt. Negant corpora

" a corporibus moveri, quod inter motum corporis, et motum" eorum in quae incidit nullus deprehendatur nexus, adeo ut

" moto corpore A, necesse sit moveri corpus B, cui colliditur.

" lidem quoque negant corpora a spiritibus moveri, quia inter

'^ voluntatem spirituum etmotumcorporuin nullum connexionem

* Or Ifkite, a Romisli priest, author of ii ticiilise eulitlrd, Sciri sire Scep-

tkcs it Sccptko7'um ujure Disi)iiiationig Exdusio. (See Biog. Diction.)


" animadvertunt, &c. Fatendum a nobis hujusmodi connexum

" nullum cerni, nee sequi ex eo quod, corpore moto, id, in quod

" incidit, movetur ; aut ex eo quod, mente volente, corpus

" agitatur, corpora et mcntem esse veras motus causas. Fieri

*' posset, ut occasiones tantum essent, quibus positis, alia causa

" ageret. Verum uti, ex ejusmodi possibilitate, non colligeris

*' rem ita se habere ; ita ne eo quod non adsequeris aliquid,

" consequens est ut nihil sit ; nisi aliunde probaveris tibi esse

" earum rerum, de quibus agitur, adsquatam ideam, aut rem*

' repugnare, &c.—Possunt inesse corporibus motis, et spiri-

*' tibus, focultates ignota;, de quibus judicium nullum, aut ne-

" gando aut affirmundo, lerre possunms. Itaque ex aequo pec-

" cant, qui affirmant inesse iis certo iacultates efficiendorum

" quorundam, quae an ab iis fiant ignorant ; et qui negant quid-

" quani inesse corporibus et spiritibus, nisi quod in iis pei'-

" spicue norunt."

—

Joannis Clcrici Opera Philosophica. Amstel.

1698. Ontol. T. I. p. 376.

After this cloud of authorities (many of which are from

books in very general circulation), it is surprising that the fol-

lowing sentence should have escaped the pen of Dr Beattie

:

*' The sea has ebbed and flowed twice every day in time past;

" therefore the sea will continue to ebb and flow twice every

** day in time to come,—is by no means a logical deduction of

" a conclusion from premises.

—

This remark was first

" MADE BY Mr Hume."—Essay on Trutli, 2d ed. p. 126.

It is evident, that this rem.ark is only a particular application

of the doctrine contained in the above quotations ; as well as

in the numerous extracts to the same purpose, collected in

Note (C.) at the end of the first volume of this work. In one

of these (from Hobbes) the very same observation is made

;

and a sort of theory is proposed to explain how the mind is thus

led to infer thejiiture from \he past ;—a theory which, how-

ever unsatisfactory for its avowed purpose, is yet sufficient to

shew, that the author was fully aware, that our expectation of

the continuance of the laws of Nature was a fact not to be ac-

counted for from the received principles of the scholastic phi-

losophy.


Note (P,) p. 374.

From the Preface of Pappus Alexandrinus to the Seventh

Book of his Mathematical Collection. (See Halley's Version

and Restitution of Apollonius Pergaeus de Sectione Rationis

et Spatii, p. xxviii.)

....'* Resolutio est methodus, qua a quaesito quasi

" jam concesso per ea quae deinde consequuntur, ad conclu-

" sionem aliquam, cujus ope Compositio fiat, pcrducamur. In

*• resolutione enim, quod quaeritur ut jam factum supponentes,

*' ex quo antecedente hoc consequatur expendimus ; iterumque

*' quodnam fuerit hujus antecedens ; atque ita deinceps, usque

" dum in hunc inodum regredientes, in aliquid jam cognitum*' locoque principii habitum incidamus. Atque hie processus

" Analysis vocatur, quasi dicas, inversa solutio. E contrario

" autera in Compositione, cognitum illud, in Resolutione ulti-

" mo loco acquisitum ut jam factum praemittentes ; et quae ibi

" consequentia erant, hie ut antecedentia naturali ordine dis-

*' ponentes, atque inter se conferentes, tandem ad Construc-

** tioneni quaesiti pervenimus. Hoc autem vocamus Synthesin.

** Duplex autem est Analyseos genus, vel enim est veri inda-

" gatrix, diciturque Theoretica ; vel propositi investigatrix,

" ac Problematica vocatur. In Theoretico autem genere,

*' quod quaeritur, revera ita se habere supponentes, ac deinde

** per ea quae consequuntur, quasi vera sint (ut sunt ex hypo-

" thesi ) argumentantes ; ad evidentera aliquam conclusionem

*' procedimus. Jam si conclusio ilia vera sit, vera quoque** est propositio de qua quaeritur ; ac demonstratio reciproce

*' respondet analysi. Si vero in falsam conclusionem inci'

*' damns, falsum quoque erit de quo quaeritur. • In Pro-

*' blematico vero genere, quod proponitur ut jam cognitum

** sistentes, per ea quae exinde consequuntur tanquam vera,

* From the account Aven iu the text of Theoretical Analysis, it Avould

seem to follow, that its advaniaês, as a methof) of investigation, increase in

proportion to tlie variety of demonstrations of wliich a theorem admits; and

tiiat, in tlie case of a theorem ailmitting of one demonstration alone, the

two nietliods would be exactly on a level. Tiie justness of this conclusion

will, J believe, be found to correspond with the experience of every persoB

conversant with the processes of the Greek geometry.

10


" perduclmur ad concliisionem uliquam : quod si conclusio ilia

" possibilis sit ac vo^tGryi, qaod Matiieinatici Datum appellant

;

" possibile quoque erit quod proponitur : et hie quoque de-

" monstratio reciproce respondebit Analysi. Si vero incida--

*' mus in conclusioneni impossibilera, erit etiam problema im-

" possibile. Diorismus autem sive determinatio est qua dis-

'' cernitur quibus conditionibus quotque modis problema ettici

" possit. Atque linec de Resolutione et Compositione dicta

« suntoi"

Note (Q.) p. 409.

The following passage from Buffon, although strongly mark-

ed with the author's characteristical spirit of system, is yet, I

presume, sufficiently correct in the outline, to justify me for

giving it a place in this note, as an illustration of what I have

said in the text on the insensible gradations which fix the li-

mits between resemblance and analogy.

" Take the skeleton of a man ; incline the bones of the pel-

** vis ; shorten those of the thighs, legs, and arms;join the

*^ phalanges of the fingers and loes ; lengthen the jaws by slort-

" ening the frontal bones ; and lastly, extend the spine of the

*' back. This skeleton would no longer represent that of a

" man ; it would be the skeleton of a horse. For, by length-

" ening the back bone and the jaws, the number of the verte-

" brae, ribs, and teeth, would be increased ; and it is only by*' the numbers of these bones, and by the prolongation, cnn-

" traction, and junction of others, that the skeleton of a horse

" differs from that of a man. The ribs, which are essen-

*' tial to the figure of animals, are found equally in man, in

" quadrupeds, in birds, in fishes, and even in the turtle. The*' foot of the horse, so apparently different from the hand'*' of a man, is composed of similar bones, and, at the extremi-

" ty of each finger, we have the same small bone resembling

" the shoe of a horse which bounds the foot of that animal.

*' Raise the skeletons of quadrupeds, from the ape kind to the

" mouse, upon their hind legs, and compare them with the

* skeleton of a man ; the mind will be instantly struck with the

VOL. II, N n


" uniformity of structure observed m the formation of the

" whole group. This uniformity is so constant, and the gra-

" dations from one species to another are so imperceptible,

" that, to discover the marks of their discrimination, requires

" the most minute attention. Even the bones of the tail will

** make but a slight impression on the observer. The tail is

" only a prolongation of the os coccygis or rump-bone, which

" is short in man. The ouran outang and true apes have no*' tail, and in the baboon and several other quadrupeds, its

" length is very inconsiderable. Thus, in the creation of ani-

" mals, the Supreme Being seems to have employed only one

*' great idea, and, at the same time, to have diversified it in

" every possible manner, that men might have an opportunity

" of admiring equall}' the magnificence of the execution, and

** the simplicity of the design."

—

Smellies Translation.

As a proof that the general conclusion in which the fore-

going extract terminates, requires some important qualifications

and restrictions, it is sufficient to subjoin a few remarks from

a later writer, who, with the comprehensive views of Buffon,

has combined a far greater degree of caution and correctness

in his scientific details.

*' It has been supposed by certain naturalists,

*' that all beings may be placed in a series or scale, beginning

*' with the most perfect, and terminating in the most simple,

" or in the one which possesses qualities the least numerous

" and most common, so that the mind, in passing along the

*' scale from one being to another, shall be nowhere conscious

" of any chasm or interval, but proceed by gradations almost

*' insensible. In reality, while we confine our attention within

" certain limits, and especially while we consider the organs

" separately, and trace them through animals of the same class

" only, we find them proceed, in their degradation, in the most

*' uniform and regular manner, and often perceive a part, or

" vestige of a part, in animals where it is of no use, and where

" it seems to have been left by Nature, only that she might not

*' transgress her general law of continuity.

" But, on the one hand, all the organs do not follow the

" same order in their degradation. This organ is at its highest


" State of perfection in one species of animals ; that organ is

" most perfect in a different species, so that, if the species are to

" be arranged after each particular organ, there must be as many** scales or series formed, as there are regulating organs assum-

" ed ; and in order to construct a general scale of perfection,

" applicable to all beings, there must be a calculation made of

" the effect resulting from each particular combination of or-

" gans,—a calculation which, it is needless to add, is hardly

*' practicable.

" On the other hand, these slight shades of difference, these

" insensible gradations, continue to be observed, only while we" confine ourselves to the same combinations of leading organs ;

** only while we direct our attention to the same great central

" springs. Within these boundaries all animals appear to be

" formed on one common plan, which serves as the ground-

" work to all the lesser internal modifications ; but the instant

" we pass to animals where the leading combinations are differ-

'' ent, the whole of the resemblance ceases at once, and we** cannot but be conscious of the abruptness of the transition.

" Whatever separate arrangements may be suitable for the

*' two great classes of animals, with and without vertebrae, it

" will be impossible to place at the end of the one series, and*' at the commencement of the other, two animals sufficiently

" resembling, to form a proper bond of connection."—Intro-

duction to Cuviers Legons d'Anatomie Comparee.

Note (R.) p. 427-

Of fortunate conjectures or hypotheses concerning the laws

of nature,many additional examples might be produced from the

scientific history of the eighteenth century. Franklin's sagacious

and confident anticipation of the identity of lightning and of

electricity is one of the most remarkable. The various analo-

gies previously remarked between their respective phenomena

had become, at this period, so striking to philosophers, that the

decisive experiment necessary to complete the theory was car-

ried into execution, in the course of the same month, on both

sides of the Atlantic. In the circumstantial details recorded

«f that made in America, there is something peculiarly interest-


ing. I transcribe them in the words of Dr Priestley, who as-

sures us that he received them from the best authority.

" After Franklin had published his method of verifying his

" hypothesis concerning the sameness of electricity with the

" matter of lightning, he was waiting for the erection of a

" spire in Philadelphia to carry his views into execution ; not

" imagining that a pointed rod, of a moderate height, could

" answer the purpose ; when it occurred to him that, by means" of a common kite, he could have a readier and better access

" to the regions of Uiunder, than by any spire whatever. Pre-

" paring, therefore, a large silk handkerchief, and two cross

" sticks of a proper length, on which to extend it, he took the

" opportunity of the first approaching thunder-storm to take a

" walk into a field, in which there was a shed convenient for

" his purpose. But dreading the ridicule which too commonly" attends unsuccessful attempts in science, he communicated

" his intended experiment to nobody but his son, who assisted

" him in raising the kite.

" The kite being raised, a considerable time elapsed before

** there was any appearance of its being electrified. One very

" promising cloud had passed over it without any effect ; when,

" at length, just as he was beginning to despair of his contri-

" vance, he observed some loose threads of the hempen string

" to stand erect, and to avoid one another, just as if they had

" been suspended on a common conductor. Struck with this

' promising appearance, he immediately presented his knuckle

" to the key, and (let the reader judge of the exquisite plea-

" sure he must have felt at that moment) the discovery was

" complete. He perceived a very evident electric spark.

" Others succeeded, even before the string was wet, so as to

" put the matter past all dispute ; and when the rain had wet

" the string, he collected electric fire very copiously. This

" happened in June 1752, a month after the electricians in

" France had verified the same theory, but before he heard of

" any thing they had Aone."—'Priestley s History of Electricity,

pp. 180, 181, 4to ed.


Note (S.) p. -lis.

*' Natural knowledge may not unaptly be compared to a ve-

" getable, whether plant or tree, which springs from a seed sowed

" in a soil proper, and adapted by a skilful gardener, for that

" plant. For as the seed, by small fibrills or roots it shoots out,

" receives from the soil or earth a nourishment proper and adapt-

" ed for ascending into the body or stalk, to make it grow in

** bulk and strength to shoot upwards, and from thence to shoot

" forth branches, and from them leaves, thereby to draw and re-

** ceive out of the air a more refined, spirituous, and enlivening

"juice, which, descending back into the body or stock, increases

" its stature, bulk, circumference, and strength, by new encir-

" clings, and thereby enables it to send forth more fibrills and

" greater roots, which afford greater and more plentiful supplies

" to the stock or trunk, and enables that to exert and shoot

" forth more branchings, and greater numbers of leaves; which,

" repeating all the effects and operations by continued and con-

" stant circulations, at length bring the plant to its full stature

" and perfection

:

" So natural knowledge doth receive its first informations from

" the supplies afforded by select and proper phenomena of nature

" conveyed by the senses ; these improve the understanding, and

" enable it to raise some branchings out into conclusions, corol-

" laries, and maxims ; these afford a nutritive and strengthenuig

" power to the understanding, and enable it to put forth new

" roots of inquisition, trials, observations, and experiments, and

" thereby to draw new supplies of information : which further

«' strengthening the understanding, enable it to exert and pro-

*' duce new deductions and new axioms : These circulate and

" descend downwards, increasing and strengthening the judgment,

" ami thereby enable it to make more striking out of roots of in-

" quiries and experiments, which cause the like effects as before,

" but more powerfully, and so by consent and continued circu-

" lations from phenomena to make deductions, and from deduc-

" tions to inquire phenomena, it brings the understandmg lo a

** comp'ete and perfect comprehension of the matter ut first

" proposed to be considered.''

—

Hooke's Posthumous IVorks^

p. 5.53.


Note (T.) p. 435.

*' Aliquando observationes ct (.xperimenta immediate nobis

*' exhibent principia, quae quaerimus ; sed aliquando etiam fiypo-

*' t/ieses in auxilium vocamus, non tanipn penitus arbitrarias, sed

" conformes lis qua; observantur, et quae supplentes immediata-

*' rum observationum defectum, viam investigationi sternuiit, tau-

" quam dtvinantibus ; uL si ea, quas ex ipsis deducuntur, inveni-

" amus re ipsa, eadem retinoamus, et progrediamur ad nova

*' consectaria ; secus vero, ipsas rcjiciamus. Et quidera ple-

*' rumque banc esse aibitror methodum omnium aptis'îmam in

" physica, quas saepissime est velut qusdam enucleatio epistolae

" arcanis notis conscriptas, ubi per attentationem, et per errores

*' etiam plurim-os paulalim et caute progrediendo, ad veram ejus

" theoriam devenitur : cujus rei specimen admodum luculentum

" exhibui in mea dissertatione de lumine, agens de rectilinea lu-

" minis propagatione ; acin Stayanas Philosophiae Tomo I., agens

" de generalibus proprietatibus corporum, et de vi inertiae in prl-

** mis ; Torao vero II. agens de totius Astronomias constitutione."

—Boscovich de Solis ac Lunce Defectibus.

In Sprat's History of the Royal Society, a similar idea occurs,

illustrated by an image equally fanciful and apposite. " It is iiot

" to be questioned, but many inventions of great moment have

" been brought forth by authors, who began upon suppositions,

" which afterwards they found to be untrue. And it frequently

** happens to philosophers, as it did to Columbus ; who firbt be-

" lieved the clouds that hovered about the Continent to be the

" firm la7id: But this mistake was happy ; for, by sailing towards

" them, he was led to what he sought ; so by prosecuting of mis-

" taken causes, with a resolution of not givmg over the pursuit,

" they have been guided to the truth itself."

[The work from which this passage is taken (it may be here

remarked, by the way) affords complete evidence of the share

which, in the judgment of the founders of the Royal Society,

Bacon had in giving a beginning to experimental pursuits in

England. See, in particular. Section xvi.]

10


Note (U.) p. 435.

With respect to the application of the method of exclusions to

physics, an important logical remark is made by Newton, in one

of his letters to Mr Oldenburgb, Obvious and trivial as it may

appear to some, it has been overlooked by various writers of great

name ; and therefore I think proper to state it in Newton's own

words.

" In the meanwhile, give me leave, Sir, to insinuate, that I

" cannot think it effectual for determining truth, to examine the

" several ways by which phenomena may be explained, unless

" ivhere there can be a perfect enumeration of all those ways,

*' You know the proper method for inquiring after the properties

" of things, is to deduce them from experiments. And I told

" you, that the theory which I propounded (concerning light

" and colours) was evinced to me, not by inferring, it is thuSf

*• because it is not otherwise ; that is, not by deducing it only

" from a confutation of contrary suppositions, but by deriving it

" from experiments concluding positively and directly. The*' way, therefore, to examine it is, by considering whether the

•* experiments which I propound, do prove those parts of the

** theory to which they are applied ; or by prosecuting other ex-

" periments which the theory may suggest for its examination,"

&c. 6cc.—Horselei/'s Edition of Newton's IVorks, Vol. IV,

p. 320.

Note (X.) p. 443.

" If we consider the infantine state of our knowledge con-

" cerning vision, light, and colours, about a century ago, very

" great advancements will appear to have been made in this

" branch of science ; and yet a philosopher of the present age*' has more desiderata, can start more difficulties, and propose

" more new subjects of inquiry, than even Alhazen or Lord Ba-" con. The reason is, that whenever a new property of any*• substance is discovered, it appears to have connections with

*' other properties, and other things, of which we could have no" idea at all before, and which are by this means but imperfect-

*' ly announced to us. Indeed, every doubt implies some degree

*' of knowledge ; and while nature is a field of such amazing,


" perhaps boundless extent, it may be cwpectcd that the more

" knowledge we gain, the more doubts and difificuUies we shall

" h;ive ; but still, since every advance I'li knowledge is a real and

" valuable acquisition to mankind, in consequence of its ena-

" bling us to apply the powers of nature to render our situation

" in life more happy, we have reason to rejoice at every new dif-

" ficulty that is started, because it informs us that more know-

" ledge and more advantage are yetunattained, and should serve

•' to quicken our diligence in the pursuit of them. Every desi-

*' deratum is an imperfect discovery"—Priestley s History of

Discoveries relating to Vision^ Light, and Colours, p. 773*

(Lond. 1772.)

Note (Y.) p, 458.

For the analogies between Galvanism and Electricity, see

Traite Elementaire de Physique, par M. L'Abbe Haiiy, § 717-

—

The passage concludes with the following remark, which may be

regarded as an additional proof, that, even when analogical con-

jectures appear to depart the most widely from the evidence of

experience, it is from experience that they derive their whole

authority over the belief. " Partout le fluide electrique semblc

" se multiplier par la diversite des phenomenes ; et il nous avait

" tellement accoutumes a ses metamorphoses, que la nouveaute

*' meme de la forme sous laquelle il s'offrait dans le Galvanisrae

" naissant, semblait etre une raison de plus pour le reconnaitre,"

Note (Z.) p. 471.

In that branch of politics which relates to the theory of Go-

vernment, one source of error (not unfrequently overlooked by the

advocates for experience) arises from the vagueness of the lan-

guage in which political facts are necessarily stated by the most

faithful i)nd correct historians. i\'o better instance of this can

be produced than the terms Monarchy, Aristocracy, and Demo-

cracy, commonly employed to distinguish different forms of Go-

vernment from each other. These words, in their strict philoso-

phical acceptation, obviously denote not actual but zWca/ constitu-

tions, existing only in the imagination of the political theorist;

while, in more popular discoursej they are used to discriminate,


according to their provailinu; bias or spirit, the various mixed es-

tablishmenls exemplified in the history of human affairs. Poly-

bius, accordinoly, with his usual discernment, expresses his

doubts, under which of the three simple forms the constitution of

Rome, at the period when he had an opportunity of studying it,

ought to be classed. " When we contemplate," he observes, " the

*' power of the Consuls, it seems to be a monarchy ; when we at-

" tend to the power of the Senate, it seems to be an aristocracy;

*' when we attend to the power of the People, we are ready to

" pronounce it a democracy." *

it is easy to see how much this scantiness and want of preci-

sion in our political vocabulary, must contribute to mislead the

judgments of those reasoners who do not analyze very accurately

the notions annexed to their words ; and, at the same time, what

a purchase they afford to the sophistry of such writers as are dis-

posed, in declamations addressed to the multitude, to take an un-

due advantage of the ambiguities of language.

Another source of error which goes far to invalidate the autho-

rity of various political maxims supposed to be founded on expc"

rience, is the infinite multiplicity of the seemingly trifling and

* This obsei valiou of Polybius has been vPiy unjustly censured by Gro-

tius. " Sed ueque Polybii liic utor auctoritate, qui ad mivtuni genus rei-

" publicae ret'eit Komanam rempublicam, quae illo tempore, si noii actiones

" ipsas, std jus (igendi respicimus, mere fuit popiilaiis : Nam et senatus

" aiictorita*, quam act optimatum regimen refeit, et consulum quos quasi

" reges fuisse vult, subdita eiat populo. Idem de aliorum polilica scriben-

*' lium senlentiis dictum voJo, qui mafjis extcrnam speciem et quotidianam

" administralioneu?, quam jus ipsuni suuimi mipeiii spectare cougruens du-

" cunt sue iijslitdto," {Dp Jure Belli ac Pacis, Lib. I. Cap. 3.) In reply

to this criticism, it is sufficient to rtmaik, tliat Polybius is not here speaking

t)f the thearij ot" tlie Roman constitution (about whicii there could be no di-

versity of opinion), but of wliat coniniOD observers are so apt to overlook,

—

the actual state of that constitution, aioditied as it was by time, and chance,

and experience.—Among the numerous commentators on Grotius, I recol-

lect one only (Henry de Cocceii) who lias viewed this question in its pro-

per light. " Auctor inter eos, qui circa formas imperii falhmtur etiam

« Polybium refeit, qui rempublicam Romanam suis teniporibus mixtam" fuisse ait At bene notandum, Polybium non loqui de mixtura statue

*' sed administrationis : forma enini reipublicae erut mere popularis, sed ad-

f minislratio divisa fuit inter consules, senatum, et populuin."


evanescent causes connected with local manners and habits,,

which, in their joint result, modify, and in some cases counteract

so powerfully, the effects of written laws and of established forms.

Of these causes no verbal description can convey an adequate

idea ; nor is it always possible, even for the most attentive and

sagacious observer, when the facts are before his eyes, to appre-

ciate all their force :—So difficult is it to seize the nicer shades

which distinguish the meanings of correspondmg terms in diftbr-

ent languages ; and to enter, at years of maturity, into those de-

licate and complex associations, which, in the mind of a well-

educated native, aie identified with the indigenous feelings of na-

tional sympathy and taste.

Of the truth of this remark, a striking illustration presents it-

self in the mutual ignorance of the French and English nations

(separated from each other by a very narrow channel, and, for

centuries past, enjoying so many opportunities of the most fami-

liar intercourse) with respect to the real import of the words and

phrases marking the analogous gradations of rank in the two

countries. The words gentil/iomme and gentleman are both deriv-

ed from the same etymological root; yet h iw imperfect a tians-

lation does the one afford of the other ! and how impossible to

convey by a definition all that is implied in either ! Among French

writers of no inconsiderable name, we meet with reasonings which

plainly shew, that they considered the relative rank of the mem-

bers of our two Houses of Parliament, as something similar to

what is expressed in their own language by the words noble and

roturier ;—while others, puzzled with the inexplicable phenomena

occasionally arising from the boundless field of ambition opened

in this fortunate island to everj' species of industry and of enter-

prise, have been led to conclude, that birth has, among us, no

other value than what it derives from the privileges secured by

the constitution to our hereditary legislators. Few perhaps but

the natives of Great Britain are fully aware, how very remote

from the truth are both these suppositions.

I transcribe the following passage from an article in the French

Encyclopedie, written by an author of some distinction both for

talents and learning ; and which, it is not impossible, may be quot-

ed at some future period in the history of the world, as an authentic


document with respect to the state of English society in the eight-

eenth century. The writer had certainly much better access to

information than was enjoyed by those to whom we are indebted

for our €xperinie7ital knowledge of the ancient systems of policy.

" En Angleterre, la loi des successions attribue aux aines dans

" les families nobles les biens immeubles, a I'exclusion des cadets

" qui n'y ont aucune part. Ces cadets sans bien cherchent a re-

" parer leurs pertes dans I'excrcice du negoce, et c'est pour eux

" un moyen presque sur de s'cnrichir. Devenus riches, ils quit-

" tent la profession, ou mfeme sans la quitter, leurs enfans ren-

" trent dans tons les droits de la noblesse de leur famille ; leurs

" aines prennent le titre de milord si leur naissance ct la posses-

" sion d'une terre pairie le leur permettent.—II faut neanraoins

" remarquer, que quelque fiere que soit la noblesse Angloise,

" lorsque les nobles entrent en apprentissage, qui selon les regle-

" mens doit etre de sept ans cntiers, jamais ils ne se couvrent de-

" vant leurs maitres, leur parlant et travaillant tete nue, quoique

" souvent le maitre soit roturier et de race marchande, et que les

*' apprentifs soient de la premiere noblesse."

—

Encyclop. Method.

Commerce, Tom. III. Article Noblesse.

Note (AA.) p. 480.

*' Metaphysicae pars secunda est finalium causarum inquisitio,

" quam non ut prastermissam, sed ut male collocatara notamus.

" Solent enim inquiri inter physica non inter metaphysica.

" Quanquam si ordinis hoc solum vitium esset, non mihi fuerit

" tanti. Ordo enim ad illustrationem pertinet, neque est ex

" substantia scientiarum. At hsec ordinis inversio defectum in-

" signem peperit, et maximam philosophiae induxit calamitatem.

" Tractatio enim causarum finalium in physicis, inquisitionem

'' causarum physicarum expulit et dejecit, efi'ecitque ut homines

^' in istiusmodi speciosis et umbratilibus causis acquiescerent,

" nee inquisitionem causarum realium, et vere physicarum,

" strenue urgerent, ingenti scientiarum detrimento Etenim

" reperio hoc factum esse non solum a Platone, qui in hoc lit-

" tore semper anchoram figit, verum etiam ab Aristotele,

" Galeno, et aliis, qui saepissime etiam ad ilia vada impingunt.

*' Etenim qui causas adduxerit hujusraodi, palpebras cum pilis pro

57^ NOTES AND ILLUSTRATIONS.

*' sepi et tallo esse, admunimciitum oculorum: Aut coriiim in ani'

" malibus finniiudinan esse ad prnpelleiidos calores et frigora :

'' Aut ossa pro colmnnis et tmbihus a natura induct, quibus Jabri-

" ea corporis innitatur : Aut folia arhorim emitti, quo fructus

'< minus patiantur a sole et rcnto : Aut nubes in sublimi fieri, ut

" terrain imbribus irrigent : Aut terrarn densari et solidariy ut sta-

" tio et mansio sit animallum : et alia similia: Is in metaphy-

" sicis non male ista aliciârit; in physicis autem nequaquam.

" Imo, quod coepimus diccro, hujusmodi sermonum discursus^

" (iiislar rcmoiarum, uti fiugunt, navibus adhaerentium) scien-

" tiariim quasi velificationcin ct progressum retardarunt, ne cur-

" sum suum tencient, ot ultciitis piogrcderentur : et jampridtm

" eft'ccprunt, ut physicarum causarum inquisitio nc^lecta deti-

'* ccret, ac silentio piaettriiTtur. Quapropler philosuphia natU'

" rails Democriti, et aliorum, qui Deum et mentem a labrica

*' rerum amovorunt; et structuram univcrsi infinitis naturae prae-

" iusionibus et tentaniontis (quas uno nomine /a/ww?, autfortunain

" vocabant) atlribuerunt ; et rerum particularium causas, ma-

'* teriaj nccessitati, sine inlerniixtione causarum linalium, assig-

" narunt; nobis videtur, quatcnus ad causas pliysicas, multo so-

" lidior fuisse, et altius in Naturam penetrasse, quam ilia Aris-

*' totelis, et I'latonis: Hanc unicam obcausam, quod illi in causis

" iinaiibus nunquam operam triverunt; hi autem eas perpetuo

" incu'.carunt. Atque magis in hac parte accusandus Aristo-

" teles quam Plato : quandoquidem funtem causarum finalium>

" Deum scilicet, omiserit, et naturam pro Deo substituerit,

" causasque ipsas finales, potius ut iogicai amator quam tlieo-

" logige, am plexus sit. Neque ha^c eo dicimus, quod causae illaj

" finales verse non suit, et inquisitione admodum dignae in specu-

" lationibus melaphysicae, sed quia dum in physicarum causarum

" possossiones excurrunt et irruunt, miscre earn provineiam de-

" populanturet vastant."

—

De Aiigm. Scient. Lib. HI. Cap. 4.

Note (BB.) p. 493.

Among the earliest opponents of Descartes' doctrine concern-

ing Final Causes, was Gassendi; a circumstance which I remark

with peculiar pleasure, as he has been so unjustly represented by

Cudworth and others, as a partisan, not only of the physicalî buf;


of the atheistical opinions of the Epicurean school. For this

charge I do not sec that thoy had the slightest pretence to urge,

but that, in common wilh Bacon, he justly considered the physi-

cal theories of Epicurus and Democritus as more analogous to the

experimental inquiries of the moderns, than the logical subtilties

of Aristotle and of the schoolmen. The following passage is

transcribed in Gassendi's own words, from his Objections to the

Meditations of Descartes.

" Quod autein a ph^sica considerattone rejicis usum causarum

"^«a/<H?w, ahii Ibrtassis occasione potuisses recte facere : at de

" Deo c^m agitur verendum profecUj, ne praicipuum aroumen-

•* turn rejicias, quodivina sapientia, providentia, potcntia, atque

" adeo existentia, lumine naturas stabiliri potest. Quippe ut

" mundum univcrsum, ut ccelum et alias ejus et pracipuas partes

" pr^teream, undenam, aut quomodo meliiis argumentare valeas,

" quam ex usu partium in plantis, in animalibus, in hominibus, in

" te ipso (aut rorpore tuo) qui similitudinem Dei geris? Videraus

" profecto magnos qu-^sque viros ex speculatione anatomica cor-

" porishumani non assurgeie modo ad Dei notitiam, sed hymnum^ quoque ipsi canere, quod omnes partes ita conformaverit, col-

*' locaveritque ad usus, ut sit omnino propter solertiam atque

" providenliam incomparabilem commendandus."—Objectiones

Quintas in Meditalionem IV. De Vero et Falso.

I do not know it it has hitherto been remarked, that Gassendi

is one of the first modern writers, by whom the following maxim,

so often repeated by later physiologists, was distinctly stated:

" Licet €x cotiformatione partium corporis humanly cnnjtcturas de-

" svmere ad functiones mere naturales." It was frojn a precipi-

tate application of this maxim, that he was led to conclude, that

man was originally destined to feed on vegetables alone ; a pro-

position which gave occasion to several memoirs by Dr Wallis

and Dr Tyson, in the Philosophical Transactions of the Royal

Society of London.

Note (CC.) p. 510.

The theories of Hume, of Paley, and of Godwin, how dif-

ferently soever they may have figured in the imaginations of their

authors, are all equally liable ta the fundamental objections

574* NOTES AND ILLUSTRATIONS.

stated in the text. The same objections are applicable to the

generous and captivating, but not always unexceptionable mo-

rality inculcated in the writings of Dr Hutcheson.—The system,

indeed, of this last philosopher, may be justly regarded as the

parent stock on which the speculations of the others have been

successively grafted.

JMr Hume entered on his Inquiries concerning Morals, at a

period when Dr Ilutchcson's literary name v.as unrivalled in

Scotland. The abstract priiiciples on which his doctrines are

founded, differ widely from those of his predecessor, and are un-

folded with far greater ingenuity, precision, and elegance. In

various instances, however, he treads vcr^ cl -stly in Dr Ilutche-

son's footsteps; and, in the final result of his reasonings, he coin-

cides with him exactly. According to both writers, a regard to

general expediency affords the only universal canon for the regu-

lation of our conduct.

It is a curious circumstance in the History of Ethics, that the

same practical rule of life, to which Dr Hutcheson was so natu-

rally and directly led by his cardinal virtue of disinterested be-

nevolence, has been inferred by Dr Paley from a theory which

resolves moral obligation entirely into prudential calculations of

individual advantage. For the very circuitous, and (in my opi-

nion) very illogical argument, whereby he has attempted to con-

nect his conclusion with his premises, I must refer to his work.*

The politicaljustice of Mr Godwin is but a new name for the

principle of general expediency or utility. " The termJustice"

he observes, " may be assumed as a general appellation for all

*' moral duty—That this appellation," he continues, " is suffi-

" cicntly expressive of the subject, will appear, if we consider

*' for a moment, mercy, gratitude, temperance, or any of those

" duties which, in looser speaking, are contradistinguished iVom

* Principles of Moral and Political Philosophy, Book ii. Chap. 1, 2, 5,

4, 5, 6.

The Tlicory of Dr Paley lias been very ably examined by Mr Gisborne,

in a treatise eutitlefl, The Principles of Moral Philosopliy investigated, and

brieily applied to the Constitution of Civil Society. (London, 1790.) Theobjections to it there stated appear to iiie quite unanswerable, and they

possess the additional merit of being urged with all the defeience so justly

due to Dr Paley's character and talents.


"justice. Why should 1 pardon tl>is criminal, remunerate this

" favour, abstiiin troni this indulifence ? If it partake of the na-

" ture of morality, it must be either right or wrong, just or un-

" just. It must tend to the benefit of the individual, either with-

" out entrenching upon, or with actual advantage to the mass of

" individuals. Either way, it benefits the whole, because indi-

*' viduals are parts of tiae whole. Therefore to do it is just, and

" to forbear it is unjust. If justice have any meaning, it is just

" that I should contribute every thing in my power to the bcne-

" fit of the whole."

—

Polit. Justice, Vol. I. pp. 80, 81.

It is manifest, that, in the foregoing extract, the duty of jus-

tice is supposed to coincide exactly as a rule of conduct with the

affection of benevolence ; whereas, according to the common use

of words, justice means that particular branch of virtue which

leads us to respect the rights of others ; a branch of virtue re-

markably distinguished from all others by this, that the observ-

ance of it may be extorted by force ; the violation of it exposing

the offender to resentment, to indignation, and to punishment.

In Mr Godwin's language, the wovA justice must cither be un-

derstood to be synonymous with general benevolence, or—as-

suming the existence of such an affection—to express the moral

Jitness of yielding, upon all occasions, to its suggestions. " It is

^'just," says Mv Godwin, " that I should contribute every thing

" in my power to the benefit ot the whole.—My benefactor ought

" to be esteemed, not because he bestowed a benefit upon me,

" but because he bestowed it upon a human being. His desert

" will be in exact proportion to the degree in which the human

" being was worthy of the distinction conferred. Thus, every

** view of the subject brings us back to the consideration of my" neighbour's moral worth, and his importance to the general

" weal, as the only standard lo determine the treatment to which

" he is entitled. Gratitude, therefore, a principle which has so )C

" often been the theme of the moralist and the poet, is no part >C" either oijustice or virtue."—Ibid. p. 84. The words jjist and ^'

justice can, in these sentences, mean nothing distinct from mo-

rally Jit or reasonable ; so that the import of the doctrine

amounts merely to the following proposition. That it is reason-

able or right, that the private benevolent affections should, upon


all occasions, yield to the more comprehensive ;—which is pre-

cisely the system of Hutcheson disguised under a different and

much more exceptionable phraseology.

This abuse of words is not without its effect in concealing from

careless readers the fallaciousness of some of the author's subse-

quent arguments ; for although the idea he professes to convey

by the tvvmjusiice, be essentially different from that commonly

annexed to it, yet he scruples not to avail himself, for his own

purpose, of the received niaxims which apply to it in its ordinary

acceptation. In discussing, for example, the validity of pro-

mises, he reasons thus :" I have promised to do something just

" and right.—This certainly I ought to perform. Why? Not'* because I promised it, but hccduse justice prescribes it. I

" have promised to bestow a sum of money upon some good and" respectable purpose. In the interval between the promise and

" my fulfilling it, a greater and nobler purpose offers itself, which

" calls with an imperious voice for my co-operation. Which" ought I to prefer ? That which best deserves my preference*

" A promise can make no alteration in the case. I ought to be

" guided by the intrinsic merit of the objects, and not by any ex-

" ternal and foreign consideration. No engagements of mine can

" change their intrinsic claims.—If every shilling of our proper-

" ty, every hour of our time, and every faculty of our mind, have

" already received their destination from the principles of imrnu*

" tablejustice, promises have no department left upon which for

" them to decide. Justice, it appears, therefore, ought to be

" done, whether we have promised it or not."—Ibid. p. 151.

It is quite evident, that, in this passagl?, the paramount supre-

macy indisputably belonging tojustice in its usual and legitimate

sense, is ascribed to it when employed as synonymous with be-

nevolence ; and of consequence,- that the tendency of the new

system, instead of extending the province oi justice, properly so

called, is to set its authority entirely aside, wherever it interferes

with views of utility. In this respect, it exhibits a complete con-

trast to ail the maxims hitherto recognised among moralists. The

rules of justice are happily compared by INIr Smith to the strict

and indispensable rules of grammar ; those of benevolence to the

more loose and general descriptions of what constitutes the siu

NOTES AND ILLUSTRATIONS. 5^7

blime and beautiful in writing that wfc meet with in the works of

critics. According to INJr Godwin, the reverse of this compari-

son is agreeable to truth ; while, at the same time, by a dexter-

ous change in the meaning of terms, he assumes the appearance

of combating for the very cause which he labours to betray.

Of the latitude with which the wordjustice had been previous-

ly used by many ethical writers, a copious and choice collection

of instances may be found in the learned and philosophical notes

subjoined by Dr Parr to his Spital Sermon. (London, 1801.)

" By none of the ancient philosophers, however," as he has well

observed, " is justice set in opposition to any other social duty ; ^^" nor did they employ the colossal weight of the term in crush-

" ing the other moral excellencies, which were equally consider-

** ed as pillars in the temple of virtue." pp. 28, 29, 30, 31.*

Note (DD.) p. 511.

As the main purpose of this section is to combat the logical

doctrine which would exclude ihe investigation of Final Causes

from natural philosophy, I have not thought it necessary to take

notice of the sceptical objections to the theological inferences

commonly deduced from it. The consideration of these proper-

ly belongs to some inquiries which I destine for the subject of a

separate Essay. On one of them alone I shall offer at present a

few brief remarks, on account of the peculiar stress laid upon it

in Air Hume's Posthumous Dialogues.

" When two species of objects," says Philo, " have always been

" observed to be conjoined together, 1 can infer, by custom, the

" existence of one wherever I see the existence of the other : and

* Having mentioned the name of this eminent person, I eagerly embrace

the opportiuiily of acknowledging llie instruction I iiave received, not only

from his various publications, but from tiie private literary rommunicalions

with which he has repeatedly favoured me. From one of tliese (containing

animadversions on some passages in my Essay on tlie Sublime) I entertain

Lopes of being permitted to make a few extracts in a future edition of that

performance. By liis candid nnd libt ral strictures, I have felt myself high-

ly honoured ; and should be proud to record, in his own words, the correc-r

tions he has suggested of certain critical and philological judgment* which;,

it is highly probable, I may have too lightly hazarded.

VOL. IK O O

.578 NOTES AND ILLUSTRATIONS.

" this I call an argumcm nom txperience. But how this argu-

*' ment can have place, where the objects, as in the present case,

" are single, individual, without parallel, or specific resemblance,

'' may be difficult to explain. And will any man tell me, with a" serious countenance, that an orderly universe must arise from

" some thought and art, like the human, because we have ex-

" perience of it ? To ascertain this reasoning, it were requisite

" that we had experience of the origin of worlds; and it is not

*' sufficient surely, that we have seen ships and cities arise from

" human art and contrivance.—Can you pretend to shew any

" similarity between the fabric of a house, and the generation of

** the universe ? Have you ever seen Nature in any such situation

" as resembles the first arrangement of the elements ? Have" worlds ever been formed under your eye ; and have you had

" leisure to observe the whole progress of the phenomenon, from

" the first appearance of order to its final consummation ? If you

" have, then cite your experience, and deliver your theory."

This celebrated argument appears to me to be little more than

an amplification of that which Xenophon puts into the mouth of

Aristodemus, in his conversation with Socrates, concerning the

existence of the Deity. " I behold,'' says he, " none of those

** governors of the world, whom you speak of; whereas here, I

*' see artists actually employed in the execution of their respec-

" tive works."—The reply of Socrates, too, is in substance the

same with what has been since retorted on Philo, by some of

]Mr Hume's opponents. " Neither, yet, Aristodemus, seest thou

" thy soul, which, however, most assuredly governs thy body :

—

" Although it may well seem, by thy manner of talking, that it

" is chance and not reason which governs thee."

Whatever additional plausibility Philo may have lent to the

argument of Aristodemus, is derived from the authority of that

much abused maxim of the inductive logic, that " all our know-

" ledge is entirely derived from experience." It is curious, that

Socrates should have touched with such precision on one of the

most important exceptions with which this maxim must be re-

ceived.' Our knowledge of our own existence as sentient and

intelligent beings, is (as I formerly endeavoured to shew) not an

inference from experience, but a fundamental law of human bc«


lief. All that experience can teach me of my internal frame,

amounts to a knowledge of the various mental operations where-

of I am conscious ; but what light does experience throw on

the origin of my notions of personality and identity ? Is it from

having observed a constant conjunction between sensations and

sentient beings ; thoughts and thinking beings ; volitions and ac-

tive beings ; that I infer the existence of that individual and

permanent mind, to which all the phenomena of my conscious-

ness belong ? Our conviction that other men are, like ourselves,

possessed of thought and reason ; together with all the judgments

we pronounce on their intellectual and moral characters, cannot

(as is still more evident) be resolved into an experimental per-

ception of the conjunction of different objects or events. They

are inferences of design from its sensible effects, exactly analo-

gous to those which, in the instance of the universe, Philo would

reject as illusions of the fancy. *

But leaving for future consideration these abstract topics, let

us, for a moment, attend to the scope and amount of Philo's

reasoning.—To those who examine it with attention it must ap-

pear obvious, that, if it proves any thing, it leads to this general

conclusion, That it would be perfectly impossible for the Deity,

if he didexht, to exhibit to Man any satisfactory evidence of cfe-

sign by the order and perfection of his works. That every thing

we see is consistent with the supposition of its being produced

* This last consideration is ably stated by Dr Reid. (See Essays on the

Intellectual Powers, pp. 631, 65'2, 4to ed.) The result of his argument

is, that, " according to Philo's reasonin</, we can have no evidence ofmmd" or design in any of our fellow-men."—At a considerably earlier period,

Buffier had fallen into the same train of thinking. Among the judgments

which he refers to common sense, he assigns the first place to the two follow-

ing :'^ 1. Ily a d'autres ctres, et d'autres hommes que moi au 7nonde. 2. II

" y a da7is eux quelque chose qui s'appelle verite, sagesse, prudence" &c. &c.

(Cours de Sciences, p. 566. Paris, 1732.) I have already objected to the

application of the phrase common sense lo sncli judgments as these; but this

defect, in point of expression, does not detract from the .sagacity of the au-

thor in perceiving, that in the conclusions we form concerning the minds

and characters of our fellow -creatures (as well as in the inferences drawn

concerning the invisible things of God from the things which are made), there

is a perception of the nnderstaiKiing implied, for which neither reasoning

nor experience is sufficieut to account.


by an intelligent author, Philo himself has explicitly acknov\r-

ledged in these remarkable words : " Supposing there were a God,

" who did not discover himself immediately to our senses ; would" it be possible for him to give stronger proofs of his existence,

" than what appear on the whole face of nature ? What, indeed,

" could such a Divine Being do, but copy the present economy of

•' things;—render many of his artifices so plain, that no stupi-

" dity could mistake them ;—afford glimpses of still greater ar-

" tifices, which demonstrate his prodigious superiority above our

" narrow apprehensions ;—and conceal altogether a great many" from such imperfect creatures ?"—The sceptical reasonings of

Philo, therefore, do not, like those of the ancient Epicureans,

hinge, in the least, on alleged disorders and imperfections in the

universe, but entirely on the impossibility, in a case to wkich

experience furnishes nothing parallel or analogous, of rendering

intelligence and design manifest to our faculties by their sen-

sible efi'ects.— In thus shifting his ground from that occupied

by his predecessors, Philo seems to me to have abandoned the

only post from which it was of much importance for his adver-

saries to dislodge him. The logical subtilties, formerly quoted

about experience and belief (even supposing them to remain un-

answered), are but little calculated to shake the authority of

principles, on which we are every moment forced to judge and

to act, by the exigencies of life. For this change in the tactics

of modern sceptics, we are evidently, in a great measure, if not

wholly, indebted to the lustre thrown on the order of nature, by

the physical researches of the two last tenturies.

Another concession extorted from Philo by the discoveries of

modern science is still more important. I need not point out its

coincidence with some remarks in the first part of this section,

on the unconscious deference often paid to final causes by those

inquirers who reject them in theory ;—a coincidence which had

totally escaped my recollection when these remarks were writ-

ten. I quote it here, chiefly as a pleasing and encouraging con-

firmation of the memorable prediction with which Newton con-

cludes his Optical Queries ; that " if Natural Philosophy^ in

" all its parts, by pursuing the inductive method, shall at

5


" length be perfected, the bounds of Moral Philosophy will be

" enlarged also.''

*' A purpose, an intention, a design," says Philo, " strikes

" everywhere the most careless, the most stupid thinker; and no

" man can be so hardened in absurd systems, as at all times to

** reject it. That Nature does nothing in vain, is a maxim esta-

" blished in all the schools, merely from the contemplation of

" the works of Nature, without any religious purpose ; and from

" a firm conviction of its truth, an anatomist, who had observed

" a new organ or canal, would never be satisfied till he had also

*' discovered its use and intention. One great foundation of the

" CoPEUNiCAN system is the maxim, That Nattire acts by the

'•' simplest methods, and chooses the most proper means to any

" end i and astronomers often, without thinking of it, lay this

" strong foundation of piety and religion. The same thing is

" observable in other parts of philosophy : And thus all the sci-

" ences lead us almost insensibly to acknowledge a first intelli-

" gent author ; and their authority is often so much the greater,

" as they do not directly profess that intention."

^ P. 106.

Since this sheet was cast off, I have been informed, from the

best authority, that the conversation here alluded to, which I had

understood to have taken place between Lord Chief Justice

Mansfield and the late Sir Basil Keith, really passed between his

Lordship and another very distinguished officer, the late gallant

and accomplished Sir Archibald Campbell. I have not, how-

ever, thought it worth while, in consequence of a mistake which

does not affect the substance of the anecdote, to cancel the leaf;

—more especially, as there is at least a possibility that the same

advice may have been given on more than one occasion.

x\PPENDIX.

Article I. (See page I71.)

The following article relates entirely to the question,—" How" far it is true, that all mathematical evidence is resolvable into

" identical propositions ?" The discussion may, in one point of

view, be regarded as chiefly verbal ; but that it is not, on that

account, of so trifling importance as might at first be imagined,

appears from the humiliating inference to which it has been sup-

posed to lead concerning the narrow limits of human knowledge." Put the question," says Diderot, " to any candid mathemati-*< cian, and he will acknowledge, that all mathematical proposi-

" tions are merely identical ; and that the numberless volumes" written (for example) on the circle, only repeat over in a hun-" dred thousand forms, that it is a figure in which all the straight

" lines drawn from the centre to the circumference are equal.*' The whole amount of our knoivledge, therefore, is next to no'" thing."—That Diderot has, in this very paradoxical conclusion,

stated his own real opinion, will not be easily believed by those

who reflect on his extensive acquaintance with mathematical andphysical science ; but I have little doubt, that he has expressed

the amount of the doctrine in question, agreeably to the inter-

pretation put on it, by the great majority of readers.

As the view of this subject which I have taken in the text,

has not been thought satisfactory by my friend M. Prevost, I

have thought it a duty, both to him and to myself, to annex to

the foregoing pages, in his own words, the remarks subjoined to

the excellent and faithful translation with which he has honouredthis part of my work, in the Bihliotlieque Britanniqiie. Amongthese remarks, there is scarcely a proposition to which I do not

give my complete assent. The only difference between us turns

on the propriety of the language in which some of them are ex-

584 APPENDIX.

pressed ; and on this point it is not surprising, if our judgmentsshould be somewhat biassed by the phraseology to which wehave been accustomed in our earher years. The few sentences

to which I am inclmed to object, I have distinguished from the

rest, by printing them in small capitals.—Such explanations of

my own argument as appear to be necessarj', 1 have thrown in-

to the form of notes, at the foot of the page.

In the course of M. Prevost's observations on the point in

question, he has introduced various original and happy illustra-

tions of the important distinction between conditional and abso-

lute truths ;—a subject on which I have the pleasure to find, that

all our views coincide exactl3\

" A la fin de I'article que Ton vient de lire, * I'ingenieux auteur

renvoie a ce qu'il a dit au commencement. II pense y avoir suf-

fisamment pi-ouve que I'evidence particuliere qui accompagne le

raisonnement mathematique ne peut pas se resoudre dans ia per-

ception de I'idcntite. Recourons done a cette preuve. EUe se

trouve consister toute entiere en refutation.

" I. L'auteur commence par remarquer, que quelques person-

nes fondent I'opinion qu'il rejette sur celle qui prend les axiomespour premiers principes. Et comme il a combattu cel!e-ci, 11 enconclut que sa consequence doit etre fausse. Un tel argument aen effet beaucoup de force pour ceux qui sonl partis d'une cer-

trine theorie sur les axiomes pour en conclure fassertion contes-

tee ; mais il n'en a point pour les autres. Le redacteur de cet

article se range parmi ces derniers. II a dit et il pense encore,

que le mathematicien avance de supposition en supposition ; quec'est en retournant sa pensee sous diverses formes, qu'il arrive a.

d'utiles resultats ; que c'est la reconnoissance de quelqueIDENTITE QUI AUTORISE CHACUNE DE SES CONCLUSIONS ; €t

toutefois il a dit et il persiste a croire, que les axiomes mathema-tiques ne font que tenir la place ou de definitions ou de theoremes ;

et que les definitions sont les seuls principes des sciences de la

nature de la geometric. Voici ses propres expressions. * " J'ob-*' serve que de bonnes definitions initiales sont les seuls principes" rigoureusement sufEsans dans les sciences de raisonnement'' pur C'est dans les definitions que sont veritablement con-*' tenues les hypotheses dont ces sciences partent On pour-" roit concevoir [toujours dans ces memes sciences], que les

*' principes fussent si nettement poses, que I'on n'y trouvat autre*' chose que de bonnes definitions. De ces definitions retournees,'* resulteroient toutes les propositions subsequentes. Les diver-

• Chap. II. Sect. 3. Art. II. of tliis volume.

t Essais de Pbitos. Tom. II. p. 29, a Geneve chez P^choud, 180*.

APPE-NDIX. 585

•* SES propbietk's du cercle que sont-elles autre chose," QUE DIVERSES FACES DE LA PROPOSITION QUI De'fINIT CETTE" courbe ?—C'cst. done I'imperfection (pcutetre inevitable) de" nos conceptions, qui a engage a faire entrer les axiomes pour*' quelque chose dans les principcs des sciences de raisonnement" pur. Et ils y font un double office. Les uns i-emplacent des

" definitions. Les autres rcmplacent des propositions suscepti-

" bles d'etre deniontrees.''

" II est manitcste que celui qui a tenu de tout temps ce langage

n'a pas f'onde son opinion, vraie ou fausse, relativenient h I'evi-

dence matheuiatique, sur une opinion fausse relativenient auxaxiomes ; ou du nioins, qu'etant si parfaitement d'accord avec

Mr Dugald Stewart en ce qui concerne les premiers principes des

mathematiques, ce n'est point de la que derive I'apparente discor-

dance de ses expressions et de celles de son ami, sur ce qui con-

cerne le principe de I'evidence mathematique dans la deduction

demonstrative. Des lors il est evident que ce premier argument

de i'auteur reste pour lui comme nul.

" IL Passons au second. Celui-ci est encore purement nega-

tifet personnel. II s'adresse a ceux qui derivent, d'un principe

propre a la geometrie, I'assertion que I'auteur combat. De ce

que I'egalite en geometrie se demontre par la congruence, ces

philosophes se pressent de conclure, que, dans toutes les mathe-matiques, les verites reposent sur I'identite. Ceux done qui n'ont

jamais songe a donner un tel appui a I'assertion contestee nepeuvent absolument pas se rendre a Tattaque dirigee contre cet

appui. II est probable qu'un tres-grand nombre de partisans duprincipe de I'identite, considere comme base de la demonstration,

se trouvent (comme le redacteur pent ici le dire de lui-meme)

tout a fait etrangers a la maniere de raisonner que I'auteur refute;

et n'ont point forme leur opinion relativement a I'evidence ma-thematique d'apres la congruence (reelle on potentielle) de deuxespaces. C'est ce que le redacteur affirme ici, quant a lui, de la

maniere la plus positive ; et de la resulte que I'argument person-

nel, * dirige contre ceux qui out ete menes d'une de ces opi-

nions a I'autre, ne I'atteint point.

" II est un peu plus difficile de prouvcr cette affirmation, quequand il etoit question des axiomes, parce que ceux-ci ne peu-vent pas manquer de s'ofFrir aux recherches du logicien, au lieu

qu'il n'est pas appele a prtvoir I'application inconsideree du prin-

cipe de superposition a toute especc de demonstration. Si ce-

pendant il fait voir que son opinion sur la demonstration derive

de principes universels et tout differens de celui qu'on a en vue,

jl aura fait, je pense, tout ce qu'il est possible d'attendre de lui,

• Ad lioiBineni,

586 APPENDIX.

" Qu'il soit maintenant perniis au redacteur de quitter lit

tierce personne, et pour eviter quelques longueurs et quelque*expressions indirectes, d'etablir nettemenl son opinion et la

marche qu'il a tenue en I'exposant.

" Des les premieres pages de ma logique, je pars de la distinc-

tion a faire entre les deux genres de verite ; la conditiotmelle et

Vabsolue. Puis j'ajoute

:

" Le moyen unique, par lequel nous connoissons si une*' pkoposition conditionnelle est vhaie, ou le caractere" d'une telle verite, est l'identite biem etablieentre le** PRINCIPE ET LA CONSEQUENCE. CeTTE IDENTITe' n'eST PAS*' complete SANS DOUTE ; MAIS ELLE EST TELLE A QUELQUE*' EGARD, QUE LA CONSEQUENCE DOIT ETRE TOUTE ENTIERE*' COMPRISE DANS LE PRINCIPE." *

" Traitant ensuite des sciences selon leur genre, j'appelle

sciences de raisonnement pur celles qui ne s'occupent que de la

verite conditionnelle. Je cherche, d'une maniere generale et ab-

straite, les caracteres de ces sciences. J'en fais ensuite I'appli-

cation aux mathematiques dans les deux branches qu'elles com-prennent ; et c'est par cette voie, que je .me trouve avoir deter-

mine la nature de la demonstration. J'ai soin du reste de faii*e

remarquer que la nature du raisonnement pur, ou proprement dit,

ne depend nullement du sujet, et qu'il n'est propre aux mathema-tiques qu'en ce sens que ces dernieres s'ocupent de raisonnement

d'une maniere exclusive et n'y melent point des propositions deverite absolue, comme font les sciences de fait et d'experience.

En voila assez, je crois, pour faire voir que ce n'est pas temeraire-

ment que j'affirme n'avoir en aucune faôn congu la nature de la

demonstration d'apres le point de vue borne de ia superposition.

Je ne puis done, quant a moi, donner mon assentiment a un ar-

gument qui n'attaque que ceux dont I'opinion a cette base." III. On est toujours long quand on refute une refutation.

J'aurois done tort de m'etendre au-dela de ce qui est stricte-

ment necessaire pour etablir nettement I'etat de la question. Je

ne discuterai pas des opinions qui me sont etrangeres, telles'que

celles de Leibnitz, de I'auteur d'une Dissertation latine impri-

* Essats de Pliil. Tom. II p. 2. ' Le lecteiir Equitable voudra bieii se rap-

peler que rouvrage, dont < e passage ost tir6, n'csl que I'esqiiisse d'nn conrs

ibit etendH, dans If^quei >e tiouvent d^veioppes, par des pxiniples ei detoute nianieip, les siniple>^ eiioncfe <lu tcxte. A peine est-il n^ci ssane dedire ici en explication ce que j'enteni's par I'i^tentite compiete on non com-plete entre le prnicipe et sa consequence. Si je conclns, par example, dugenre a I'pspece, il y a iilentii^ inroniplete ; omme lorsqn'ayant pronv^ unev4rit6 de tout polygene, j« I'affirine tin triangle en particidier. II y a iden-

lile conplele dans niie Equation. Et on entend bien que I'identiie dontil s'agit est celle de la qnantiie (^du nonibrt- des unites), et non de toute antre.

Ces deux exemples me sem blent suffire pour prtvenir toute Equivoque."

APPENDIX. 587

mee a Berlin en J 764?, de Barron-, Condillac, Destutt- Tracy. IJ

me suffit d'avoir repondu, pour moi et pour ceux qui pensent

comme nioi, aux deux seuls arguniens de I'auteur, centre I'opi-

nion que j'ai des long-temps adoptee." J'ajouterai cependant un mot au sujet d'une remarque, que

I'auteur introduit en disant, qu'elle est applicablê h ioutes les ten-

iatives que Von ajaites pour etabllr Vopinion dont ils'agit. " Ac-" cordant, dit-il, que toutes les propositions matheniatiques puis-" sent etre representees par la f'ormule a = «, il ne s'ensuivroit

" nullement que chaque pas du raisonnement, qui conduit a ces" conclusions, soit une proposition de meme nature." Je pric

I'auteur de cette objection de vouloir bein reflechir un instant

sur le sens du mot pas ramene ti son expression propre et non fi-

guree. Certainement un pas du raisontiement n'est autre chose

qu'une proposition. Si done on accorde que toute proposition est

representee par a zz a, il faudra bien que tout pas soit de memenature.

*

" Quant a la lettre chifFree, certainement elle difFere de la non-chifFree quant aux signes ecrits ; comme aussi les plus exageres

partisans du principe de I'identite ne nieront pas que I'expression

deux plus deux ne soit difterente de I'expression quatre. DansPun et I'autre cas le signe difFere, le sens que Ton a en vue est le

meme." IV. Les observations precedentes ont pour but de prouver

que, dans les precedes de raisonnement (precedes que les mathe-matiques ofFrent degages de tout melange,) on deduit les conse-

quences en s'appuyant constarament sur le principe d'identite'.

Je dois dire un mot maintenant de la raison pour laquelle je crois

necessaire d'etablir solidement ce principe et de la mettre au-des-

sus de tout attaque. Cette raison est, qu'a I'instant ou on le

perd de vue, on court risque de confondre deux genres de veri-

tes, que nous savons tous qu'il faut distinguer. Ce qu'il importe

de prevenir, c'est le passage inaperû du relatif a I'absolu ; c'est

* That the word yus or step is a figurative expression, when npplied to aprocess of reasoning, cannot be disputed ; and the same remark may be ex-tended to the word proposition, and to almost every otlier tenn employed in

discussions connected with the Human Mind. It may be doubted, however,whether it can be coirectly asserted, tJuit a step of reasoning differs in no re-

spect from a proposition. In our langnasie, at least, the word step properly

denotes, not a proposition, but the transition to a new piopositiou from others

already known. Thus, when I say, " tlie area of a triangle, having the cir-

" cumference of a circle for its base, and the ladius for its altitude, is greater" than the area of any polygon inscribed in the circle," I enunciate a proposi-

tion. When I say, that " the area of the same triangle is less than that of any** circimistribed polygon," I enunciate another proposition. ]>ut wben I in-

fer from these two propositions, that the areas of the triangle and circle areequal, I obtain possession of a new truth distinct from either; nor is it easy to

imagine a more significant metaphor for expressing this acquisition, than to

say, that I have advanced or gained a step in the study of geometry.

588 APPENDIX*

une conclusion vicieuse, deduite regulierement d'une hypothese,et tcmerairement appliquee a. ce qui est independant de cette hy-pothese. Ce sophisme, qui paroit grossier, a neanmoins etecomrais plus d'une fois et le sera, dans quelques occasons decep-trices, par ceux qui n'auront pas pleinement analyse le travail duraisonnement.

" Tout se reduit, sans doute, en fait de raisonnement, a recon-noitre que la consequence est bien deduite du principe. Maisquel est le caractere auqucl on reconnoitra que cette deductiona ete bien faite ? C'est ce que ne disent pas ceux qui rejettent

Is caractere de I'identite. Et j'avoue que je ne congois pas quelautre on pourroit tenter d'y substituer. Celui-la est simpleET CLAIR. • On peut, a chaque proposition, s'arreter pour voir

si elle n'est que le developpement d'une precedente ; et si, parinadvertance on sort du genre, en raelant des faits aux hypothe-ses, on est ramene forcement a celles-ci.

" Si Jean Bernouilli et Leibnitz avoient reconnu leurs hypo-theses aussi nettement qu'Euler les reconnut plus tard, ils n'au-

roient pas ete divises d'opinion sur la nature des logarithmes des

nombres negatifs et imaginaires. Si Huyghens n'avoit vu, dansle travail du mathematicien, que le retournement de ses propreshypotheses, il ne se seroit pas servi peut-etre de I'expression querapporte Leibnitz. Ce dernier lui ayant montre, qu'une quan-tite melee d'imaginaires pouvoit etre convertie en quantite reelle,

" Huyghens, dit Leibnitz, trouva cela si admirable, qu'il me re-*' pondit qu'il y a la-dedans quelque chose qui nous est incompre-*' hensible." f

" Je connois un professeur de logique, qui a coutume, dans ses

cours, d'embarrasser a dessein ses eleves par des questions rela-

tives aux rapports des qaantites negatives et positives. Si unparadoxe les arrete, ils se tiennent pour avertis, qu'il ne peut yavoir dans les consequences, que ce qui est implicitement contenudans le principe ; et ils se donnent le soin de bien afFermir celui-

ci, je veux dire, de le reduire a des termes parfaitement clairs;

apres quoi, il ne leur en coute point de lever les difficultes.

Mais si Ton n'est pas bien preoccupe de cette verite fondamen-tale, on ne saura a quoi imputer I'anomalie, ou I'apparente con-

tradiction, des consequences." Personne n'adraire plus sincercment que je ne fais le genie

de Jaq. Bernouilli, qu'il a si heureusement applique a la theorie

des probabilites ; et je ne fais certainement aucune injure a sa

niemoire, en le produisant comme un exeraple de la facilite avec

laquelle le mathematicien, seduit par ses belles decouvertes, oublie

* Would it not be still simpler and clearer to caution mathematicians against

ever losing sight of Ihe distiuction between absolute and hypothetical truths?

t Leibnitz. Opera, Tom. III. p. 372. Leltre a Varignon.

APPENDIX. 589

un instant quel est le genre de verite qui lui est propre. J'ai en

vue la dernierc reflection de son Art de conjecturer. D'une fbr-

mule (tres-belie sans doute et tres-ingenieuse) par laquclle ce

prolbnd penseur a apprecie la probabilite d'approcher du rapport

des causes en multipliant les effets ; tout-a-coup il conclut a la

regularite des lois que gouvernent I'univers. *

" On ne me reprochera pas d'avoir tire mes exemples des ecrits

de quelques raisonneurs mediocres; et Ton voudra bien croire,

que si j'avois voulu puiser a de telles sources, j'aurois eu beau-coup de I'acilite a multiplier mes citations.

" Je pense done enfin, qu'il faut que celui qui travaille dans les

sciences de raisonnement pur soit bien averti, qu'il ne fait autre

chose que retourner ses hypotheses, et que c'est la le seul moyende prevenir des erreurs assez dangereuses. L'opinion que je sou-

tiens n'est done point simplement une affaire de speculation, dontil me seroit aise de faire le sacrifice ; c'est une regie pratique qui

doit servir de base a la partie de la logique qui s'occupe de cette

espece de verite.

*' V. Je dirai maintenant pourquoi, attache comme je lesuis, Au PRINCIPE DE l'identite, je crois neanmoins pouvoir

esperer de ne difFerer qu'en apparence de I'excellent philosophe

qui rejette ce principe. C'est parce que nous pensons I'un et

I'autre que les definitions sent les Trais principes des mathema-tiques, et que tout le reste en derive. C'est la sansôute I'objet

principal. Et je m'assure, que quand ce philosophe viendra adiscuter (avec plus de detail que son sujet ne I'appeloit a le faire)

le vrai caractere de la bonne deduction, il finira par admettre, si-

non les memes expressions, du moins au fond le meme principe

que j'emploie.

" Je vois en efFet, et par son ouvrage et par sa correspondance,

que ce sent les expressions sur-tout qu'il censure ; et quant a cepoint la, je serai tres-dispose a y apporter les changemens qu'il

voudra bien lui-meme me suggerer, pourvu toutefois qu'elles ren-

dent correctement ma pensee." Ainsi apres lui avoir expose, dans une lettre, mes idees au

sujet du principe d'identite, j'ajoutois : " Tout cela revient a*' dire, que la consequence est contenue toute entiere dans le

" principe. Ne pourroit-on pas dormer a toutes les propositions" mathematiques cette tournure : Dire telle chose, cest dire tellt.

* Unde tandem Iioc singulare sequi videtnr, qiiod si eventuiiin omnium ob-servation's per lotam aeteniiiatem ooiiiinoaieutur (piobabilitate ullirao in

peifectam ceiiitr.diuL'in abeuute), omnia in miindo cutis latiouibus et coii-

staiiti vicissiiudinis lege couliojêre deprehendereiitur ; adco lit, eliaiii in

iDaxime casiialibiis atque fortiiilis, qua;.dam quasi neccssitatem, et, ut sic di-

oanijtatalilaleni agiiosceie teneamur; quam uesciD aimon Plato intendere vo-hierir, suo de iiniveisali lerum apocalastasi dogmale, etc. Art. conj. p. 4.,

fine.

590 APPENDIX.

" metre chose?" Mr Dugald Stewart me repond la-dessus: " Je" suis parfaitement d'accord avec vous, quant a I'esprit et a la

" substance de votre remarque. Celui qui adraet la definition ou*' Vhypothese ne peut pas nier ses diverses consequences logiques,

'' pourvu qu'il soit en etat de comprendre chaque pas de la marche" par laquelle le principe et les consequences sont lies ensemble." Je ne suis pas sur toutefois que, pour le gros des lecteurs, vous" ne presentiez pas cette proposition d'une maniere trop concise'' et trop figuree, quand vous dites que la consequence est con-

" te.nuc dans le principe, ou qu'affirnier Tun c'est affirmer I'autre.

" Tout au moins je pense quil y a lieu de craindre que ces ex-" pressions ne suggerentde tausses idees a. ceux qui neprendront" pas garde au sens precis que vous donnez aux mots que vous*' employez." Je suis done tout pret a reniplacer le mot contennc

par un equivalent. Mais ce mot me semble pris ici dans un sens

familier aux logiciens ; car c'est precisement ainsi que Ton dit

communement que I'espece est comprise dans le genre. *

" Un autre mot, que releve Mr Dugald Stewart, est celui deproposition identique.j- II me fait remarquer, que plusieurs bons

logiciens ont appele de ce nom les propositions qui ne font que

repeter le meme mot aux deux termes (A est A), et qu'ils desig-

nent ces propositions comme inutiles et nugatoires. Je renon-

cerai sans discussion, sur I'autorite de ces logiciens, a I'expres-

sion que j'ai* adoptee, quoique je puisse opposer autorite a auto-

rite. Mais je desire conserver un mot qui exprime, de maniere

* " Si Ton peut dire que la notion de triangle Mt comprise dans celle depolygene, on pourra dire de certaines propositions sur les triangles qu'eHes

sonl comprises dans leurs analogues sur les polygone*. Si done on a prouv^%

par exemple, que dans tout polygone, les angles exterieiirs sont egaux a

qnatre droits, on pourra de ce pnncipe tirer la consequence pour les triangles.

Et celte consequence semble pouvoir etre dite contenue dans son principe."

With this remark I perfectly agree; for he who knows tlie general theorem

is in actual possession of all its particular cases ; insomuch that, after lliii

theorem has been once brought to light, no other person can afterwards lay

claim to any one of the cases as an original discovery. After it had been demon-strated, for instance, that in every rectilineal figure, the exterior angles are

equal to four right angles, no geometer could well think of aimouncing, as n

new proposition, that the same theorem holds with respect to every triangle.

The particular cast\s, therefore, may all be said, with perfect propriety, to becontained in the general theorem. But how widely does this ditler from the

meaning annexed to the same word, when it is said, that all the properties of

the cncle, whether discovered or undiscovered, are contained in Euclid's deti-

nition of that curve?

t " Mr Dui;al!l Stewart reproche aussi quelque part au mot d'idetiiitS d'etre

emprunte des scolasliques, mais ce n'est point la une tache a mon avis; car

(comme disoit Leibnitz en parodiant un mot dc Virgile ;) il y a de for dan*

ce fumier. De plus en Anglais on pourroil peut-etre se passer de ce mot, enFran9ais on ne le peut pas. Nous pa;ious une langue timide, qui s'ctfraje dumoindre ucologisme.''

10

APPENDIX. 591

ou d'autre, ma pensee. Comme dit Campbell, • cette phrase

" quatre est quatre," n'ofFre qu'une proposition inutile et verita-

blement nugatoire. Mais dire " deux fois deux font quatre,"

c'est presenter la meme idee sous deux faces ; et un tel travail

est, comme on salt, fort utile. Je ni'etois accoutume h, appeler

tautologiques les premieres, et identiques les secondes. Je suis

tout pret a changer cette habitude, pourvu que Ton me fournisse

un mot a substituer. \" Enfin Mr Dugald Stewart joint a ces critiques une remarque,

qui fait voir qu'un des motifs, pour lesquels il s'est eleve centre le

principe d'identite, est la crainte qu'il n'entraine dans quelques

consequences fausses ou meme dangereuses. Voici comme il

s'exprime sur la fin de la lettre, dont je viens d"extraire les ob-

servations precedentes :" A toutes ces propositions, comme votes

" les entendez, je souscris sans difficulte. Mais n'est-il pas a*' craindre qu'elles ne fassent naitre dans I'esprit de quelques lec-

" teurs des idees differentes de celles que vous y attachez ? Et*' n'ont-elles pas une tendance a donner un air paradoxal a une" doctrine, qui, lors-qu'eile est proposee d'une maniere un peu" pleine, ne donne aucune prise au doute ou a I'hesitation ? Quelle" etrange consequence a ete tiree de I'usage de ce mot idcntite.,

" par un philosophe, tel que Diderot! Interrogez, dit-il, des ma-" thematiciens de bonnefoi- et Us voiis avoueront que leurs fropO'** sitions sont toutes identiques ; et que tant de volumes sur le cerclCf

* Voyez Bibl. Brit. p. 32 de ce volume.—Litteiaf. Vol. LVIII. No. 3,

Mars 1815.

f The distinction marked in Uie above passaije, between tautological andidentical propositions is precise and important ; but (he meaniriji annexed to

the latter epitliet docs not appear to mr agreeable to established use ; accord-

infj to which, identical propositions are exactly of that description to which the

uame of tautological is here applied. 1 liave looked into every book of logic

within my reach, and find their language on tins subject perfectly uniform.

Locke defines identical propositions to be those in which a leim is affiimed ofitself; and he gives as instances, " a soul is .1 soul," " a spirit is a spirit," " a' law is a law," *' right is right," an*' " wrong is wrong."—The definition ofidentical propositions given by Cronsaz comcides exactly with that of Locke

:

" Quando subjecti et attributi sedem idem occupat terminus, eodem sensu" prorsus veniens

;propositio talis dicitur identica ; et nugaioria est."—Con-

diliac, one of the highest authoiities, certainly, among French logicians, ex-

presses himself in the same manner. " Tout le s\steme des connoissances" humaiues peut-etre rendu par une expression plus abr^gee et tont-a-fait

"identique: les sensations srmi des sensatio7is. Si nous pouvioiis, daws /ouffs•' les sciences, suivre ^galeuient la generation des idês, et saisir le vrai sys-

" teme des choses, uohs verrions d'line verity naitre toutes les autrcs, et nous" trouverions Texpression abr^gê de tout <f que nous saurions, dans cette" proposition identique ; LE meme est le smeme." Does not the last of these

propositions, as well as the first, fall undei the class of tautological or nugatorypropositions ? and, if this be the case, will it not follow, that the assertion

which gave rise to this discussion requires some modification ?—" C'est en i^'-

*' p^tant sans cesse, It v\ime est k mime, que le gômetre opere lous ses pro-'* diges,"

592 APPENDIX.

•' par exemple, se reduisent a nous repeter en cent millefagons dif-

^^ferentes, que cest unefgure, ou toutes les lignes iirees du centre" a la circonference sont egales. Nous ne savons donc puesque" RIEN." *

" Cette derniere conclusion, a laquelle arrive Diderot, est

d'autant plus etrange, comme le dit celui que la cite, que c'est

precisement parce que les mathematiques travaillent sur la verite

conditionnelle, qu'elles sont douees d'une pleine certitude, ainsi

que jai tache de la faire voir ailleurs, -)• et que c'est par conse-

quent a ce titre qu'elles meritent tininemment le nom de science.

Mais de ce qu'un philosophe, tel que Diderot, s'est egare dansune consequence %'laquelle sans doute il aspiroit, je ne crois pasque Ton doive conclure a la necessite de changer un langagephilosophique et conforme a la verite. Si ce langage a une ap-parence de paradoxe, ce que je ne sens pas, il faut tacher de la

reformer, a quoi je suis bien dispose a cooperer." Dans tout le volume que j'extrais, il n'est plus question de la

discussion qui vient de nous occuper. Je ne crois pas en conse-quence avoir occasion d'y revenir. Ce n'est pas meme sans re-

gret, et sans une sorte de repugnance, que je I'ai entreprise. Jene la terminerai pas sans rappeller encore une fois que Tespeced'opposition qui regne entre nos opinions est moins reellc qu'ap-

parente, et que Mr Dugald Stewart a juge lui-meme que c'etoit

iur les mots que nous differions, plutot que sur le fond dcsehoses."

Article II. (See page S9.Q.)

For the contents of this Article, as well as of the former, I

am indebted to M. Prevost. They are extracted from a letter,

dated Geneva, &th April 1815.—My readers will thus be put in

possession of the opinion of my learned friend on the only twoquestions of any moment which we have had occasion to discuss

in the course of our long literary correspondence. The difference

between us, in botii instances, I perfectly agree with him in think-

ing, is more apparent than real.

" Mais il y a une autre question sur laquelle nous difFerons,

ou du moins nous ne nous exprimons pas de meme. C'est ce

qu'etublit d'une maniere positive, et dans des expressions bien

honorables pour moi, la note qui se trouve au bas de la page 3\\%

* Lellre sur les avou^les.

Dcs Sijrnes, p. 15 et '2:> et siiiv.—Essaiide Pliilos. Tom. II. p. 10 et I.'i.

i Page ;>-'t) of tliis edition.

APPENDIX. 593

de ce meme 2d volume de vos Elem. of the Phil. iSrc.—Ce qu'il ya de singulier, c'est qu'encoreici, j'ai lieu de croire que notre dis-

senthnent est moins reel qu'apparent, et que la controverse sur

ce point n'est pas moins verbale que sur I'autre, peut-etre plus,

ou du moins plus evidemment telle. La chose vaut la peine

d'etre- eclaircie.—Et d'abord, vu la distance qui nous separe,

oserois-je vous prier de relire ici ce que je dis a la page viii et ix

de ma preface a la traduction de votre premier volume. Vous yverrez que je n'etablis aucune difference entre nous relativement

a la nature des causes physiques.* En citant a la p. 31 If du2d vol. les deux phrases aux quelles vous reduisez mes opinions

a ce sujet, il vous a echappe que la premiere de ces phrases etoit

iQodifiee par celle qui la suit et que vous avez omise. Cette

modification est tout-a-fait essentielle. " Si Ion analyse le mot'\ force on e?iergie, et qu'on se borne aux causes naturelles ; on" verra que cela signifie que I'effet suit constamment la cause par" quelque loi de la nature." Dans mes cours d'enseignement,

j'insiste beaucoup sur cette definition, a laquelle je ne crois pas

que (dans vos idees telles que je les connois) vous ayez rien a

objecter. Elle presente en effet le meme caractere des causes

physiques que Hume et vous ; et elle repond en meme temps a,

une difficulte de Reid, tres-fondee si on n'y met aucune limite.

Est-il besoin avec vous de details et d'exemples ? Je ne le pense

pas. Cependant la crainte d'etre obscur me fera ajouter un mot.

A la nouvelle lune de Mars, les Mahometans se tiennent prets a

voir, et des qu'ils raper9oivent ils jettent un cri. Ce cri est bien

• The passage here referred to I)y M. Prevost is as follows

:

" Je n'eiitoml pas toutefois souscrire implicitement a toutes les opinions de

Tauteur. Je ine suis prescril dans cette traduction de rendre fideleraent ses

pensces, et je n'ai pas era devoir {oiijours lui oi>poser les miennes, dans les

CMS lares on je ne me Ironvois pas d'accord avec Ini, J'en doiinerai un seul

exeniple. L'auteur envisage comme contraire aux pi incipes d'une saine piii-

losophie la leclierciie de la cause ou da mecanisme de la gravitation. Ceux(j.'ii ont connoissance des Iravaux entrepris et executes par G. L. Le SageS11! cette inaticic, saveiit qii'nne telle recherciie est compatibl" avec la m6-tiiode philosophiquc la plus lisjomeuse. Je snis pleinenient d'accord avec

M. Stewart, quant a la leiile fjenerale a laquelle ccile maxime particuliere se

rapporte. II y a nne limite, que le philosoplie tloit r; connoitre, et audela delaquelle il ne doit pas pousser ses rcclieiclifs. Mais je diflfere sur la place ou

cette limite doit ctre posee ; en conveuant loiitefois, qne la recherche da me-canisme de la icravitation a etc I'occasion il'ime multitude d'erreurs, et que(•'est uii veritable ccueil qui doit etre soinneusement ^vite par ceux qui d^butent

daiis la carriere des sciences piiilosopiii(pies. Quoique cette question soit

tres interessante en physique, elle I'est moins en metaphysique, on plut6t en

lr)j5iqne;puisque dans cette derniere sciciice ce n'est qu'uu exemple d'une

regie qui a beaucoup d'applications. Par cetle raison,je m'abstiendrai d'entrer

ici dans ia discussion de ce point confestc."

t Page 329 of this edition.

VOL, 11. P p

594 APPENDIX.

un signe, mais non line cause de I'apparition que j'aurai devantles yeux en les tournant vers le ciel. II precede, mais ce n'est

pas en vertu d'une loi. Reciproquement, un corps electrique

etant frotte un autre corps s'en approche, je dis indifFeremmentque I'un de ces corps attire I'autre, ou que I'electricite est causede ce mouvement. C'est que ces faits se suivent en vertu deslois de I'electricite. Et il est entendu que Ton remonte, tant queTon pout, de cause en cause. Ainsi Ton pourroit demander la

cause de I'electricite ; comme on pourroit demander celle de la

fievre, qui elle-meme est cause du delire, &c. &c. Je dis doneque nous sommes pleinement d'accord sur la nature des causes

physiques, a moins (ce que je ne prevois pas) que vous ne mecontestiez la distinction que j'etablis entre cause et signe.—Lepoint sur lequel nous ne somvnes pas d'accord (et ou j'ai contra

moi, outre vous, plusieurs nobles autorites) est une question dephysique pure ; savoir : la cause de la gravitation est-elle aunonibre de celles dont on doit s'occuper ? Persistons a cet egardchacun dans notre opinion. II est probable que ce champ dediscussion ne nous engagera pas dans une controverse directe, et

je m'en feliciterai.—Je passe a remarquer la difference entre loi

et cause. Une loi est un rapport, ou mieux, un rapport de rap*

ports, une proportion. C'est une chose theorique ; c'est une ge-

neralisation ; une loi ne pent agir. II faut done un agent ; unecause, pour i-ealiser un changement. Exemple. *' Si le pole*' nord d'un aimant est approche du pole sud d'un autre ainmnt," il y a attraction." C'est une loi, Mais ce simple enonce ne

produit rien. Maintenant j'ai sur ma table deux aimans, j'oppose

leurs poles antagonistes ; la cause y est ; I'attraction (ou approche)

suivra d'apres la loi J'ai risijue de proposer que le mot agent

fut plus particulierement consacre aux causes impulsives, parce-

qu'elles sont celles qui produisent des phenomtnes tres communs,tres-bien discutes, et universels. Je n'ai propose cela qu'avec

une expression de doute; et je n'ai ricn a dire a ceux qui s'y re-

fusent.—Pour mieux montrer que la distinction de loi et cause

est necessaire en physique, j'userai d'un exemple. Un homme,venu de je ne sais ou, voit un cheval qui traine un chariot ; mais

il n'aperôit point ies traits. A chaque pas que fait le cheval, il

voit le cliariot avancer.* II en conclut que le cheval est cause

du mouvement du chariot. II penetre plus avant et trouve les

traits ; il reconnoit que ce mouvement se rapporte a I'impulsion.

Tout cela suppose qu'il connoit les lois de celles-ci. Le cheval

est une cause, le trait est une cause plus reculee. C'est celle-ci

que j'appellerois un agent. Mais pour cette derniere denoraina-

* II est enlcndu que ce fait se repute souvent d'ime maniere uniforme sup

phisienrs chariots pareils et itîalivement sur chacnti.

5

APPENDIX. 595

tion je nc dois pas trop y tenir.—Quant a la fiction de Boscovich,

purement hypothetique ; j'avoue que je ne vois pas qu'elle soit

d'un grand poids en faveur de ceux qui inculpent la recherche de

la cause de la gravitation. J'aurois sur ce sujet plus a dire

;

mais comnie c'est purement un point de physique, il me semble

que je puis ici m'en abstenir."

THE END.

Printed by George Ramsay & Co.

E<linJnirgli, 1816.

ERRATA.I'aae 44, line 5, delete jieneral

57, 28, for m'l'tonne read m'^tonne138, 10, for belli read bien

196, 10, note, /or ia read on224, 12, delete so

227, 5, note, /or propress read progress

299, 22, note, /or brevi rt-ad brevis

334, 12, note, insert parenthesis

366, 11, note, /or uiiiveialis read universalis

430, 8, note, after est insert a comma431, 6, for anticipation read anticipations

Documents

Dugald Stewart - Elements of The Philosophy Of the Human Mind Volume 2